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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>   non  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>   non  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">sr</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">Wmin</font> =  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Emax</font> =  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Nbo</font> =  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Ebo</font> =  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">Sbo</font> =  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">Wbo</font> =  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">SW</font> =  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">FiP</font> =  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c12">LaP</font> =  <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c13">g</font> = <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">h</font> = <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<a NAME="E1:57"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T5" title="JORDAN1F:th.5">JORDAN1F:5</a></span>;<br/>
<a NAME="E2:57"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T21" title="SPRECT_1:th.21">SPRECT_1:21</a></span>;<br/>
<a NAME="E3:57"/><span class="kw">then </span>
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan6.html#T1" title="JORDAN6:th.1">JORDAN6:1</a></span>;<br/>
<a NAME="E4:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A3</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<a NAME="E5:57"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="jordan6.html#T1" title="JORDAN6:th.1">JORDAN6:1</a></span>;<br/>
<a NAME="E6:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">GCw</font> = <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<span class="p1">(<span class="default"><a href="jordan1a.html#K1" title="JORDAN1A:func.1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>);<br/>
<a NAME="E7:57"/><span class="lab"><font color="Green" title="E51">A5</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="jordan1a.html#K1" title="JORDAN1A:func.1">Center</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1b.html#T11" title="JORDAN1B:th.11">JORDAN1B:11</a></span>;<br/>
<a NAME="E8:57"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>;<br/>
<a NAME="E9:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<span class="p2">(<span class="default"><a href="jordan1a.html#K1" title="JORDAN1A:func.1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57"><span class="lab"><font color="Green" title="E51">A5</font></span></a>, <a class="ref" href="jordan1a.html#T70" title="JORDAN1A:th.70">JORDAN1A:70</a>, <a class="ref" href="jordan1b.html#T13" title="JORDAN1B:th.13">JORDAN1B:13</a></span>;<br/>
<a NAME="E10:57"/><span class="lab"><font color="Green" title="E53">A7</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#T30" title="PSCOMP_1:th.30">PSCOMP_1:30</a></span>;<br/>
<a NAME="E11:57"/><span class="lab"><font color="Green" title="E54">A8</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">RevL</font> = <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>;<br/>
<a NAME="E12:57"/><span class="lab"><font color="Green" title="E55">A9</font></span>: 
( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T93" title="FINSEQ_3:th.93">FINSEQ_3:93</a></span>;<br/>
<a NAME="E13:57"/><span class="lab"><font color="Green" title="E56">A10</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T48" title="FINSEQ_5:th.48">FINSEQ_5:48</a></span>;<br/>
<a NAME="E14:57"/><span class="lab"><font color="Green" title="E57">A11</font></span>: 
( <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T6" title="JORDAN1F:th.6">JORDAN1F:6</a>, <a class="ref" href="jordan1f.html#T8" title="JORDAN1F:th.8">JORDAN1F:8</a></span>;<br/>
<a NAME="E15:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A12</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>, <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#T25" title="TOPREAL1:th.25">TOPREAL1:25</a></span>;<br/>
<a NAME="E16:57"/><span class="lab"><font color="Green" title="E59">A13</font></span>: 
4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan8.html#T10" title="JORDAN8:th.10">JORDAN8:10</a></span>;<br/>
<a NAME="E17:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A14</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E18:57"/><span class="lab"><font color="Green" title="E61">A15</font></span>: 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T31" title="SPRECT_1:th.31">SPRECT_1:31</a></span>;<br/>
<a NAME="E19:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A16</font></span>: 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T226" title="XREAL_1:th.226">XREAL_1:226</a></span>;<br/>
<a NAME="E20:57"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:57"><span class="lab"><font color="Green" title="E57">A11</font></span></a>, <a class="ref" href="jordan5b.html#T14" title="JORDAN5B:th.14">JORDAN5B:14</a>, <a class="ref" href="topreal1.html#T25" title="TOPREAL1:th.25">TOPREAL1:25</a></span>;<br/>
<a NAME="E21:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A17</font></span>: 
(  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="txt" href="#E6:57"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="ref" href="jordan6.html#T49" title="JORDAN6:th.49">JORDAN6:49</a></span>;<br/>
<a NAME="E22:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A18</font></span>: 
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:57"><span class="lab"><font color="Green" title="E58">A12</font></span></a>, <a class="ref" href="jordan5c.html#D2" title="JORDAN5C:def.2">JORDAN5C:def 2</a></span>;<br/>
<a NAME="E23:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A19</font></span>: 
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E24:57"/><span class="kw">then </span>
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E25:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A20</font></span>: 
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T13" title="JORDAN1E:th.13">JORDAN1E:13</a></span>;<br/>
<span class="kw">assume </span><a NAME="E26:57"/><span class="lab"><font color="Green" title="E67">A21</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> </span><br/>

<a NAME="E27:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A22</font></span>: 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1g.html#T47" target="_self" title="JORDAN1G:th.47">Th55</a></span>;<br/>
<a NAME="E28:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A23</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T20" title="FINSEQ_4:th.20">FINSEQ_4:20</a></span>;<br/>
<a NAME="E29:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A24</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E30:57"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:57"><span class="lab"><font color="Green" title="E59">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E31:57"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<span class="p2">(<span class="default"><a href="jordan1a.html#K1" title="JORDAN1A:func.1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="ref" href="jordan1g.html#T35" target="_self" title="JORDAN1G:th.35">Th43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1g.html#T33" target="_self" title="JORDAN1G:th.33">Th41</a></span>
;<br/>
<a NAME="E33:57"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<span class="p1">(<span class="default"><a href="jordan1a.html#K1" title="JORDAN1A:func.1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:57"><span class="lab"><font color="Green" title="E52">A6</font></span></a>, <a class="ref" href="euclid.html#T53" title="EUCLID:th.53">EUCLID:53</a></span>;<br/>
<a NAME="E34:57"/><span class="kw">then </span>
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57"><span class="lab"><font color="Green" title="E51">A5</font></span></a>, <a class="txt" href="#E17:57"><span class="lab"><font color="Green" title="E60">A14</font></span></a>, <a class="ref" href="jordan1g.html#T43" target="_self" title="JORDAN1G:th.43">Th51</a>, <a class="ref" href="jordan1b.html#T15" title="JORDAN1B:th.15">JORDAN1B:15</a></span>;<br/>
<a NAME="E35:57"/><span class="kw">then </span>
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T57" title="FINSEQ_5:th.57">FINSEQ_5:57</a></span>;<br/>
<a NAME="E36:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A25</font></span>: 
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:57"><span class="lab"><font color="Green" title="E56">A10</font></span></a></span>;<br/>
<a NAME="E37:57"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<a NAME="E38:57"/><span class="kw">then </span>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:57"><span class="lab"><font color="Green" title="E54">A8</font></span></a>, <a class="ref" href="sprect_1.html#T32" title="SPRECT_1:th.32">SPRECT_1:32</a></span>;<br/>
<a NAME="E39:57"/><span class="kw">then </span>
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E40:57"/><span class="kw">then </span>
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/>
<a NAME="E41:57"/><span class="kw">then </span>
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:57"><span class="lab"><font color="Green" title="E71">A25</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E42:57"/><span class="kw">then </span>
 not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T31" title="FINSEQ_1:th.31">FINSEQ_1:31</a></span>;<br/>
<a NAME="E43:57"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T50" title="ZFMISC_1:th.50">ZFMISC_1:50</a></span>;<br/>
<a NAME="E44:57"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E45:57"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/>
<a NAME="E46:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A26</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E47:57"/>
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="ref" href="jordan1g.html#T48" target="_self" title="JORDAN1G:th.48">Th56</a></span>;<br/>
<a NAME="E48:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A27</font></span>: 
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T57" title="FINSEQ_5:th.57">FINSEQ_5:57</a></span>;<br/>
<a NAME="E49:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A28</font></span>: 
 not <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T47" title="FINSEQ_5:th.47">FINSEQ_5:47</a></span>;<br/>
<a NAME="E50:57"/><span class="lab"><font color="Green" title="E75">A29</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T42" title="FINSEQ_5:th.42">FINSEQ_5:42</a></span>;<br/>
<a NAME="E51:57"/><span class="lab"><font color="Green" title="E76">A30</font></span>: 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T7" title="JORDAN1F:th.7">JORDAN1F:7</a></span>;<br/>
<a NAME="E52:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A31</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="topreal1.html#T25" title="TOPREAL1:th.25">TOPREAL1:25</a></span>;<br/>
<a NAME="E53:57"/><span class="lab"><font color="Green" title="E78">A32</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:57"><span class="lab"><font color="Green" title="E61">A15</font></span></a>, <a class="ref" href="xreal_1.html#T226" title="XREAL_1:th.226">XREAL_1:226</a></span>;<br/>
<a NAME="E54:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A33</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<a NAME="E55:57"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<a NAME="E56:57"/><span class="kw">then </span>
(  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:57"><span class="lab"><font color="Green" title="E77">A31</font></span></a>, <a class="txt" href="#E54:57"><span class="lab"><font color="Green" title="E79">A33</font></span></a>, <a class="ref" href="jordan6.html#T49" title="JORDAN6:th.49">JORDAN6:49</a></span>;<br/>
<a NAME="E57:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A34</font></span>: 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:57"><span class="lab"><font color="Green" title="E77">A31</font></span></a>, <a class="ref" href="jordan5c.html#D1" title="JORDAN5C:def.1">JORDAN5C:def 1</a></span>;<br/>
<a NAME="E58:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A35</font></span>: 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E59:57"/><span class="kw">then </span>
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E60:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A36</font></span>: 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T13" title="JORDAN1E:th.13">JORDAN1E:13</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c17">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c17">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> implies (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> ) )</span><br/><span class="kw">assume </span><a NAME="E1:57_2"/>
<font color="Maroon" title="c17">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E2:57_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/><a NAME="E3:57_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:57_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A37</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>;<br/><a NAME="E5:57_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E6:57_2"/>
(  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T21" title="SPRECT_1:th.21">SPRECT_1:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E7:57_2"/>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_2"><span class="lab"><font color="Green" title="E83">A37</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E8:57_2"/>
(  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:57"><span class="lab"><font color="Green" title="E82">A36</font></span></a>, <a class="ref" href="pscomp_1.html#T24" title="PSCOMP_1:th.24">PSCOMP_1:24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E62:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A38</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</a></span>;<br/>
<a NAME="E63:57"/><span class="lab"><font color="Green" title="E84">A39</font></span>: 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:57"><span class="lab"><font color="Green" title="E80">A34</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E64:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A40</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan6.html#T31" title="JORDAN6:th.31">JORDAN6:31</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:57_3"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:57_3"/><span class="lab"><font color="Green" title="E86">A41</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/><a NAME="E4:57_3"/>
( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> &amp; <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_3"><span class="lab"><font color="Green" title="E86">A41</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E5:57_3"/><span class="kw">then </span>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:57_3"/><span class="kw">then </span>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="ref" href="jordan1g.html#T53" target="_self" title="JORDAN1G:th.53">Th61</a></span>;<br/><span class="kw">hence </span><a NAME="E7:57_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E66:57"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E67:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A42</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/>
<a NAME="E68:57"/><span class="lab"><font color="Green" title="E87">A43</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E69:57"/>
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:57"><span class="lab"><font color="Green" title="E64">A18</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E70:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A44</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan6.html#T31" title="JORDAN6:th.31">JORDAN6:31</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E89">A45</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:57_4"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:57_4"/><span class="kw">then </span>
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="ref" href="topreal3.html#T6" title="TOPREAL3:th.6">TOPREAL3:6</a></span>;<br/><a NAME="E3:57_4"/><span class="kw">then </span>
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:57"><span class="lab"><font color="Green" title="E81">A35</font></span></a>, <a class="txt" href="#E23:57"><span class="lab"><font color="Green" title="E65">A19</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E4:57_4"/><span class="kw">then </span>
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T16" title="JORDAN1E:th.16">JORDAN1E:16</a></span>;<br/><a NAME="E5:57_4"/><span class="kw">then </span>
(  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> or  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E6:57_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E72:57"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T15" title="JORDAN1E:th.15">JORDAN1E:15</a></span>;<br/>
<a NAME="E73:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A46</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E74:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A47</font></span>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E92">A48</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_2.html#T9" title="SPRECT_2:th.9">SPRECT_2:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>
;<br/>
<a NAME="E76:57"/>
2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:57_6"/>
2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:57_6"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>;<br/>
<a NAME="E3:57_6"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1g.html#T31" target="_self" title="JORDAN1G:th.31">Th39</a></span>;<br/>
<a NAME="E4:57_6"/><span class="kw">then </span>
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:57"><span class="lab"><font color="Green" title="E84">A39</font></span></a>, <a class="ref" href="jordan6.html#T31" title="JORDAN6:th.31">JORDAN6:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:57_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T31" title="SPRECT_1:th.31">SPRECT_1:31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E77:57"/><span class="kw">then </span>
 <a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>) is  <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:57"><span class="lab"><font color="Green" title="E90">A46</font></span></a>, <a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="ref" href="jordan3.html#T6" title="JORDAN3:th.6">JORDAN3:6</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">g</font> = <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>   <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:57"><span class="lab"><font color="Green" title="E86">A42</font></span></a>, <a class="txt" href="#E75:57"><span class="lab"><font color="Green" title="E92">A48</font></span></a>, <a class="txt" href="#E12:57"><span class="lab"><font color="Green" title="E55">A9</font></span></a>, <a class="ref" href="finseq_3.html#T91" title="FINSEQ_3:th.91">FINSEQ_3:91</a>, <a class="ref" href="goboard2.html#T8" title="GOBOARD2:th.8">GOBOARD2:8</a></span>;<br/>
<a NAME="E79:57"/>
 <a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>) <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="jordan1e.html#T17" title="JORDAN1E:th.17">JORDAN1E:17</a>, <a class="ref" href="sprect_2.html#T22" title="SPRECT_2:th.22">SPRECT_2:22</a></span>;<br/>
<a NAME="E80:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A49</font></span>: 
<font color="Maroon" title="c17">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:57"><span class="lab"><font color="Green" title="E83">A38</font></span></a>, <a class="ref" href="sprect_2.html#T24" title="SPRECT_2:th.24">SPRECT_2:24</a></span>;<br/>
<span class="lab"><font color="Green" title="E94">A50</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c17">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_3.html#T1" title="SPRECT_3:th.1">SPRECT_3:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" title="FINSEQ_1:th.39">FINSEQ_1:39</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>
<br/>.= 
 <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
;<br/>
<a NAME="E82:57"/><span class="lab"><font color="Green" title="E95">A51</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_2.html#T5" title="SPRECT_2:th.5">SPRECT_2:5</a></span>;<br/>
<a NAME="E83:57"/><span class="kw">then </span>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c17">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T68" title="FINSEQ_4:th.68">FINSEQ_4:68</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_2.html#T8" title="SPRECT_2:th.8">SPRECT_2:8</a></span>
<br/>.= 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1g.html#T31" target="_self" title="JORDAN1G:th.31">Th39</a></span>
;<br/>
<a NAME="E85:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A52</font></span>: 
<font color="Maroon" title="c17">g</font> <a href="sprect_2.html#R2" title="SPRECT_2:pred.2">is_a_h.c._for</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:57"><span class="lab"><font color="Green" title="E93">A49</font></span></a>, <a class="txt" href="#E81:57"><span class="lab"><font color="Green" title="E94">A50</font></span></a>, <a class="ref" href="sprect_2.html#D2" title="SPRECT_2:def.2">SPRECT_2:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E86:57"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E87:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A53</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E71:57"><span class="lab"><font color="Green" title="E89">A45</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/>
<a NAME="E88:57"/><span class="lab"><font color="Green" title="E98">A54</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1g.html#T39" target="_self" title="JORDAN1G:th.39">Th47</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1"/>
(  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> or  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1"/><span class="lab"><font color="Green" title="E99">A55</font></span>: 
 <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1"/>
 not  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:57_9_1_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#T29" title="PSCOMP_1:th.29">PSCOMP_1:29</a></span>;<br/>
<a NAME="E2:57_9_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A56</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_1"><span class="lab"><font color="Green" title="E99">A55</font></span></a>, <a class="ref" href="topreal3.html#T6" title="TOPREAL3:th.6">TOPREAL3:6</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:57_9_1_1_1"/>
 <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:57_9_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A57</font></span>: 
 <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E88:57"><span class="lab"><font color="Green" title="E98">A54</font></span></a></span>;<br/>
<a NAME="E5:57_9_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="goboard7.html#T34" title="GOBOARD7:th.34">GOBOARD7:34</a></span>;<br/>
<a NAME="E6:57_9_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A58</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_2.html#T18" title="SPPOL_2:th.18">SPPOL_2:18</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E7:57_9_1_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<a NAME="E8:57_9_1_1_1"/><span class="kw">then </span>
 <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">W-most</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_1_1"><span class="lab"><font color="Green" title="E101">A57</font></span></a>, <a class="txt" href="#E6:57_9_1_1_1"><span class="lab"><font color="Green" title="E102">A58</font></span></a>, <a class="ref" href="sprect_2.html#T12" title="SPRECT_2:th.12">SPRECT_2:12</a></span>;<br/>
<a NAME="E9:57_9_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#T31" title="PSCOMP_1:th.31">PSCOMP_1:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:57_9_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:57"><span class="lab"><font color="Green" title="E53">A7</font></span></a>, <a class="txt" href="#E2:57_9_1_1_1"><span class="lab"><font color="Green" title="E100">A56</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:57_9_1_1"/><span class="kw">then </span>
 not  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T57" title="FINSEQ_5:th.57">FINSEQ_5:57</a></span>;<br/><a NAME="E4:57_9_1_1"/><span class="kw">then </span>
 not  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:57"><span class="lab"><font color="Green" title="E56">A10</font></span></a></span>;<br/><a NAME="E5:57_9_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T50" title="ZFMISC_1:th.50">ZFMISC_1:50</a></span>;<br/><a NAME="E6:57_9_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><a NAME="E7:57_9_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/><a NAME="E8:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A59</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><a NAME="E9:57_9_1_1"/>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T93" title="FINSEQ_3:th.93">FINSEQ_3:93</a></span>;<br/><a NAME="E10:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A60</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:57_9_1_1"><span class="lab"><font color="Green" title="E100">A59</font></span></a>, <a class="ref" href="finseq_3.html#T91" title="FINSEQ_3:th.91">FINSEQ_3:91</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c18">FiP2</font> =  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c19">midU</font> =  <a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>);<br/><span class="kw">reconsider </span><font color="Maroon" title="c20">RevLS</font> =  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> as   <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ;<br/><span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" title="FINSEQ_1:th.39">FINSEQ_1:39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>
<br/>.= 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T8" title="JORDAN1F:th.8">JORDAN1F:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T65" title="FINSEQ_5:th.65">FINSEQ_5:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T44" title="FINSEQ_5:th.44">FINSEQ_5:44</a></span>
;<br/><a NAME="E13:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A62</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">RevLS</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="goboard2.html#T8" title="GOBOARD2:th.8">GOBOARD2:8</a></span>;<br/><a NAME="E14:57_9_1_1"/>
 not <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T47" title="FINSEQ_5:th.47">FINSEQ_5:47</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A63</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p5">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_3.html#T1" title="SPRECT_3:th.1">SPRECT_3:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T42" title="FINSEQ_5:th.42">FINSEQ_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T45" title="FINSEQ_5:th.45">FINSEQ_5:45</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>
;<br/><a NAME="E16:57_9_1_1"/>
( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T93" title="FINSEQ_3:th.93">FINSEQ_3:93</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">h</font> = <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>   <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:57"><span class="lab"><font color="Green" title="E72">A26</font></span></a>, <a class="txt" href="#E10:57_9_1_1"><span class="lab"><font color="Green" title="E101">A60</font></span></a>, <a class="txt" href="#E15:57_9_1_1"><span class="lab"><font color="Green" title="E103">A63</font></span></a>, <a class="txt" href="#E13:57_9_1_1"><span class="lab"><font color="Green" title="E102">A62</font></span></a>, <a class="ref" href="finseq_3.html#T91" title="FINSEQ_3:th.91">FINSEQ_3:91</a>, <a class="ref" href="goboard2.html#T8" title="GOBOARD2:th.8">GOBOARD2:8</a></span>;<br/><a NAME="E18:57_9_1_1"/><span class="lab"><font color="Green" title="E104">A64</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c22">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> implies (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> ) )</span><br/><span class="kw">assume </span><a NAME="E1:57_9_1_1_4"/>
<font color="Maroon" title="c22">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E2:57_9_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/><a NAME="E3:57_9_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:57_9_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A65</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>;<br/><a NAME="E5:57_9_1_1_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E6:57_9_1_1_4"/>
(  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T21" title="SPRECT_1:th.21">SPRECT_1:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E7:57_9_1_1_4"/>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_1_4"><span class="lab"><font color="Green" title="E105">A65</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E8:57_9_1_1_4"/>
(  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T22" title="SPRECT_1:th.22">SPRECT_1:22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E20:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A66</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</a></span>;<br/><span class="lab"><font color="Green" title="E106">A67</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T42" title="FINSEQ_5:th.42">FINSEQ_5:42</a></span>
<br/>.= 
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T45" title="FINSEQ_5:th.45">FINSEQ_5:45</a></span>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c22">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> implies (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> ) )</span><br/><a NAME="E1:57_9_1_1_6"/><span class="lab"><font color="Green" title="E107">A68</font></span>: 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T21" title="SPRECT_1:th.21">SPRECT_1:21</a></span>;<br/><span class="kw">assume </span><a NAME="E2:57_9_1_1_6"/>
<font color="Maroon" title="c22">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E3:57_9_1_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c22">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/><a NAME="E4:57_9_1_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c22">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:57_9_1_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A69</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>;<br/><a NAME="E6:57_9_1_1_6"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E7:57_9_1_1_6"/>
(  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_1_6"><span class="lab"><font color="Green" title="E107">A68</font></span></a>, <a class="ref" href="jordan6.html#T1" title="JORDAN6:th.1">JORDAN6:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E8:57_9_1_1_6"/>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:57_9_1_1_6"><span class="lab"><font color="Green" title="E108">A69</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E9:57_9_1_1_6"/>
(  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c22">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T22" title="SPRECT_1:th.22">SPRECT_1:22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E23:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E107">A70</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</a></span>;<br/><a NAME="E24:57_9_1_1"/><span class="lab"><font color="Green" title="E108">A71</font></span>: 
(  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> &amp;  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:57"><span class="lab"><font color="Green" title="E58">A12</font></span></a>, <a class="txt" href="#E21:57"><span class="lab"><font color="Green" title="E63">A17</font></span></a>, <a class="ref" href="jordan5c.html#T18" title="JORDAN5C:th.18">JORDAN5C:18</a>, <a class="ref" href="sppol_2.html#T22" title="SPPOL_2:th.22">SPPOL_2:22</a></span>;<br/><a NAME="E25:57_9_1_1"/>
 <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T18" title="JORDAN1E:th.18">JORDAN1E:18</a>, <a class="ref" href="sprect_3.html#T51" title="SPRECT_3:th.51">SPRECT_3:51</a></span>;<br/><a NAME="E26:57_9_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="jordan1e.html#T1" title="JORDAN1E:th.1">JORDAN1E:1</a></span>;<br/><a NAME="E27:57_9_1_1"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:57_9_1_1"><span class="lab"><font color="Green" title="E105">A66</font></span></a>, <a class="ref" href="sprect_2.html#T24" title="SPRECT_2:th.24">SPRECT_2:24</a></span>;<br/><a NAME="E28:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A72</font></span>: 
<font color="Maroon" title="c21">h</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:57_9_1_1"><span class="lab"><font color="Green" title="E107">A70</font></span></a>, <a class="ref" href="sprect_2.html#T24" title="SPRECT_2:th.24">SPRECT_2:24</a></span>;<br/><a NAME="E29:57_9_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T8" title="FINSEQ_5:th.8">FINSEQ_5:8</a></span>;<br/><a NAME="E30:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A73</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E31:57_9_1_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c21">h</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></span>;<br/><a NAME="E32:57_9_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">A74</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c21">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:57_9_1_1"><span class="lab"><font color="Green" title="E110">A73</font></span></a>, <a class="ref" href="finseq_6.html#T109" title="FINSEQ_6:th.109">FINSEQ_6:109</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T15" title="FINSEQ_5:th.15">FINSEQ_5:15</a></span>
<br/>.= 
 <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
;<br/><a NAME="E34:57_9_1_1"/><span class="lab"><font color="Green" title="E112">A75</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c21">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T16" title="FINSEQ_2:th.16">FINSEQ_2:16</a></span>;<br/><a NAME="E35:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A76</font></span>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c21">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:57_9_1_1"><span class="lab"><font color="Green" title="E110">A73</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E36:57_9_1_1"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T13" title="JORDAN1E:th.13">JORDAN1E:13</a></span>;<br/><a NAME="E37:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E114">A77</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><span class="lab"><font color="Green" title="E115">A78</font></span>: <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_2.html#T9" title="SPRECT_2:th.9">SPRECT_2:9</a></span>
<br/>.= 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>
;<br/><a NAME="E39:57_9_1_1"/><span class="lab"><font color="Green" title="E116">A79</font></span>: 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="finseq_6.html#T42" title="FINSEQ_6:th.42">FINSEQ_6:42</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_9"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:57_9_1_1_9"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_6.html#T43" title="FINSEQ_6:th.43">FINSEQ_6:43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T5" title="JORDAN1F:th.5">JORDAN1F:5</a></span>
;<br/><a NAME="E3:57_9_1_1_9"/><span class="kw">then </span>
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="txt" href="#E39:57_9_1_1"><span class="lab"><font color="Green" title="E116">A79</font></span></a>, <a class="ref" href="finseq_5.html#T9" title="FINSEQ_5:th.9">FINSEQ_5:9</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_9_1_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E41:57_9_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E42:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E117">A80</font></span>: 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E43:57_9_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T19" title="XREAL_1:th.19">XREAL_1:19</a></span>;<br/><a NAME="E44:57_9_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E118">A81</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E42:57_9_1_1"><span class="lab"><font color="Green" title="E117">A80</font></span></a>, <a class="ref" href="jordan4.html#T8" title="JORDAN4:th.8">JORDAN4:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>

;<br/><a NAME="E46:57_9_1_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:57"><span class="lab"><font color="Green" title="E74">A28</font></span></a>, <a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A82</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T68" title="FINSEQ_4:th.68">FINSEQ_4:68</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T44" title="FINSEQ_5:th.44">FINSEQ_5:44</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T65" title="FINSEQ_5:th.65">FINSEQ_5:65</a></span>
<br/>.= 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T8" title="JORDAN1F:th.8">JORDAN1F:8</a></span>
;<br/><a NAME="E48:57_9_1_1"/><span class="lab"><font color="Green" title="E120">A83</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#T30" title="PSCOMP_1:th.30">PSCOMP_1:30</a></span>;<br/><a NAME="E49:57_9_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T16" title="FINSEQ_2:th.16">FINSEQ_2:16</a></span>;<br/><a NAME="E50:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A84</font></span>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E82:57"><span class="lab"><font color="Green" title="E95">A51</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E51:57_9_1_1"/><span class="lab"><font color="Green" title="E122">A85</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c17">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sppol_2.html#T19" title="SPPOL_2:th.19">SPPOL_2:19</a>, <a class="ref" href="sprect_2.html#T7" title="SPRECT_2:th.7">SPRECT_2:7</a></span>;<br/><a NAME="E52:57_9_1_1"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="sppol_2.html#T24" title="SPPOL_2:th.24">SPPOL_2:24</a></span>;<br/><a NAME="E53:57_9_1_1"/><span class="kw">then </span>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E54:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E123">A86</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_2.html#T22" title="SPPOL_2:th.22">SPPOL_2:22</a></span>;<br/><a NAME="E55:57_9_1_1"/><span class="lab"><font color="Green" title="E124">A87</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:57"><span class="lab"><font color="Green" title="E66">A20</font></span></a>, <a class="ref" href="pscomp_1.html#T24" title="PSCOMP_1:th.24">PSCOMP_1:24</a></span>;<br/><a NAME="E56:57_9_1_1"/><span class="lab"><font color="Green" title="E125">A88</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><a NAME="E57:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E126">A89</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T15" title="SPPOL_1:th.15">SPPOL_1:15</a></span>;<br/><a NAME="E58:57_9_1_1"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><a NAME="E59:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E127">A90</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a></span>;<br/><a NAME="E60:57_9_1_1"/><span class="lab"><font color="Green" title="E128">A91</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_3.html#T18" title="SPRECT_3:th.18">SPRECT_3:18</a></span>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c21">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c21">h</font></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:57_9_1_1"><span class="lab"><font color="Green" title="E112">A75</font></span></a>, <a class="ref" href="finseq_4.html#T67" title="FINSEQ_4:th.67">FINSEQ_4:67</a></span>
<br/>.= 
 <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
;<br/><a NAME="E62:57_9_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">h</font> <a href="sprect_2.html#R3" title="SPRECT_2:pred.3">is_a_v.c._for</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:57_9_1_1"><span class="lab"><font color="Green" title="E109">A72</font></span></a>, <a class="txt" href="#E33:57_9_1_1"><span class="lab"><font color="Green" title="E111">A74</font></span></a>, <a class="ref" href="sprect_2.html#D3" title="SPRECT_2:def.3">SPRECT_2:def 3</a></span>;<br/><a NAME="E63:57_9_1_1"/><span class="kw">then </span>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c17">g</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c21">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E85:57"><span class="lab"><font color="Green" title="E96">A52</font></span></a>, <a class="txt" href="#E35:57_9_1_1"><span class="lab"><font color="Green" title="E113">A76</font></span></a>, <a class="txt" href="#E50:57_9_1_1"><span class="lab"><font color="Green" title="E121">A84</font></span></a>, <a class="ref" href="sprect_2.html#T29" title="SPRECT_2:th.29">SPRECT_2:29</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E65:57_9_1_1"/><span class="lab"><font color="Green" title="E129">A92</font></span>: 
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c17">g</font>
 <span class="kw">and </span><br/><a NAME="E66:57_9_1_1"/><span class="lab"><font color="Green" title="E130">A93</font></span>: 
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c21">h</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c23">x</font> = <font color="Maroon" title="c22">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:57_9_1_1"><span class="lab"><font color="Green" title="E129">A92</font></span></a></span>;<br/> <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c21">h</font> = 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p5">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_2.html#T20" title="SPPOL_2:th.20">SPPOL_2:20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p2">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p5">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p5">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p0">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T47" title="FINSEQ_5:th.47">FINSEQ_5:47</a>, <a class="ref" href="sppol_2.html#T19" title="SPPOL_2:th.19">SPPOL_2:19</a></span>
;<br/><a NAME="E69:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E131">A94</font></span>: 
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>) or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p5">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:57_9_1_1"><span class="lab"><font color="Green" title="E130">A93</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E70:57_9_1_1"/><span class="lab"><font color="Green" title="E132">A95</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#T29" title="PSCOMP_1:th.29">PSCOMP_1:29</a></span>;<br/><a NAME="E71:57_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E133">A96</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1"/>
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>) or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E69:57_9_1_1"><span class="lab"><font color="Green" title="E131">A94</font></span></a>, <a class="txt" href="#E47:57_9_1_1"><span class="lab"><font color="Green" title="E119">A82</font></span></a>, <a class="txt" href="#E21:57_9_1_1"><span class="lab"><font color="Green" title="E106">A67</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_1"/><span class="lab"><font color="Green" title="E134">A97</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E135">A98</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57_9_1_1"><span class="lab"><font color="Green" title="E120">A83</font></span></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_1"/><span class="lab"><font color="Green" title="E136">A99</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E71:57_9_1_1"><span class="lab"><font color="Green" title="E133">A96</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_1"><span class="lab"><font color="Green" title="E134">A97</font></span></a>, <a class="ref" href="sppol_1.html#T41" title="SPPOL_1:th.41">SPPOL_1:41</a></span>;<br/><a NAME="E4:57_9_1_1_14_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E137">A100</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1_1_1_1"/>
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:57_9_1_1"><span class="lab"><font color="Green" title="E129">A92</font></span></a>, <a class="txt" href="#E51:57_9_1_1"><span class="lab"><font color="Green" title="E122">A85</font></span></a>, <a class="txt" href="#E38:57_9_1_1"><span class="lab"><font color="Green" title="E115">A78</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_1_1_1_1"/><span class="lab"><font color="Green" title="E138">A101</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:57_9_1_1"><span class="lab"><font color="Green" title="E128">A91</font></span></a></span>;<br/><a NAME="E3:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">W-most</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:57_9_1_1"><span class="lab"><font color="Green" title="E114">A77</font></span></a>, <a class="txt" href="#E3:57_9_1_1_14_1_1"><span class="lab"><font color="Green" title="E136">A99</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a>, <a class="ref" href="sprect_2.html#T12" title="SPRECT_2:th.12">SPRECT_2:12</a></span>;<br/><a NAME="E4:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#T31" title="PSCOMP_1:th.31">PSCOMP_1:31</a></span>;<br/><a NAME="E5:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_9_1_1_14_1_1"><span class="lab"><font color="Green" title="E135">A98</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E6:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57_9_1_1"><span class="lab"><font color="Green" title="E132">A95</font></span></a>, <a class="txt" href="#E3:57_9_1_1_14_1_1"><span class="lab"><font color="Green" title="E136">A99</font></span></a>, <a class="ref" href="topreal3.html#T6" title="TOPREAL3:th.6">TOPREAL3:6</a></span>;<br/><a NAME="E7:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:57"><span class="lab"><font color="Green" title="E90">A46</font></span></a>, <a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_1_1_1_1"><span class="lab"><font color="Green" title="E138">A101</font></span></a>, <a class="ref" href="jordan1g.html#T37" target="_self" title="JORDAN1G:th.37">Th45</a></span>;<br/><a NAME="E8:57_9_1_1_14_1_1_1_1_1"/><span class="kw">then </span>
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>;<br/><span class="kw">hence </span><a NAME="E9:57_9_1_1_14_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_1_1_1_2"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:57_9_1_1_14_1_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E18:57_9_1_1"><span class="lab"><font color="Green" title="E104">A64</font></span></a>, <a class="txt" href="#E4:57_9_1_1_14_1_1"><span class="lab"><font color="Green" title="E137">A100</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:57_9_1_1_14_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2"/><span class="lab"><font color="Green" title="E134">A102</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1_2_1_1"/>
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:57_9_1_1"><span class="lab"><font color="Green" title="E129">A92</font></span></a>, <a class="txt" href="#E51:57_9_1_1"><span class="lab"><font color="Green" title="E122">A85</font></span></a>, <a class="txt" href="#E38:57_9_1_1"><span class="lab"><font color="Green" title="E115">A78</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2_1_1_1"/><span class="lab"><font color="Green" title="E135">A103</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:57_9_1_1"><span class="lab"><font color="Green" title="E128">A91</font></span></a>, <a class="txt" href="#E54:57_9_1_1"><span class="lab"><font color="Green" title="E123">A86</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_2"><span class="lab"><font color="Green" title="E134">A102</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E136">A104</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T16" title="JORDAN1E:th.16">JORDAN1E:16</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1_2_1_1_1_1_1"/>
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_9_1_1_14_1_2_1_1_1"><span class="lab"><font color="Green" title="E136">A104</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2_1_1_1_1_1_1"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:57"><span class="lab"><font color="Green" title="E90">A46</font></span></a>, <a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_2_1_1_1"><span class="lab"><font color="Green" title="E135">A103</font></span></a>, <a class="ref" href="jordan1g.html#T37" target="_self" title="JORDAN1G:th.37">Th45</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_9_1_1_14_1_2_1_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2_1_1_1_1_1_2"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:57"><span class="lab"><font color="Green" title="E90">A46</font></span></a>, <a class="txt" href="#E51:57"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_2_1_1_1"><span class="lab"><font color="Green" title="E135">A103</font></span></a>, <a class="ref" href="jordan1g.html#T38" target="_self" title="JORDAN1G:th.38">Th46</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:57"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_9_1_1_14_1_2_1_1_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:57_9_1_1_14_1_2_1_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2_1_1_2"/><span class="lab"><font color="Green" title="E135">A105</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_2_1_1_2"/>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:57_9_1_1"><span class="lab"><font color="Green" title="E125">A88</font></span></a>, <a class="ref" href="sppol_1.html#T15" title="SPPOL_1:th.15">SPPOL_1:15</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E136">A106</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E135">A105</font></span></a>, <a class="ref" href="sppol_1.html#T40" title="SPPOL_1:th.40">SPPOL_1:40</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c24">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E5:57_9_1_1_14_1_2_1_1_2"/><span class="lab"><font color="Green" title="E137">A107</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">i</font>
 <span class="kw">and </span><br/><a NAME="E6:57_9_1_1_14_1_2_1_1_2"/><span class="lab"><font color="Green" title="E138">A108</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:57_9_1_1_14_1_2_1_1_2"/><span class="lab"><font color="Green" title="E139">A109</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_1_14_1_2"><span class="lab"><font color="Green" title="E134">A102</font></span></a>, <a class="ref" href="sppol_2.html#T14" title="SPPOL_2:th.14">SPPOL_2:14</a></span>;<br/><a NAME="E8:57_9_1_1_14_1_2_1_1_2"/><span class="lab"><font color="Green" title="E140">A110</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E138">A108</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E9:57_9_1_1_14_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E141">A111</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E24:57_9_1_1"><span class="lab"><font color="Green" title="E108">A71</font></span></a>, <a class="txt" href="#E5:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E137">A107</font></span></a>, <a class="ref" href="jordan1g.html#T52" target="_self" title="JORDAN1G:th.52">Th60</a></span>;<br/><a NAME="E10:57_9_1_1_14_1_2_1_1_2"/>
<font color="Maroon" title="c24">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E5:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E137">A107</font></span></a>, <a class="txt" href="#E8:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E140">A110</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E11:57_9_1_1_14_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E142">A112</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T43" title="FINSEQ_5:th.43">FINSEQ_5:43</a></span>;<br/><a NAME="E12:57_9_1_1_14_1_2_1_1_2"/>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E13:57_9_1_1_14_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E6:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E138">A108</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E14:57_9_1_1_14_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E143">A113</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T43" title="FINSEQ_5:th.43">FINSEQ_5:43</a></span>;<br/><a NAME="E15:57_9_1_1_14_1_2_1_1_2"/><span class="lab"><font color="Green" title="E144">A114</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c23">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E18:57_9_1_1"><span class="lab"><font color="Green" title="E104">A64</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E135">A105</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1_2_1_1_2_1_1"/>
( <font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> or <font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E138">A108</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E145">A115</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_2_1_1_2_1_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  )
 ;<br/><a NAME="E3:57_9_1_1_14_1_2_1_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E146">A116</font></span>: 
( <font color="Maroon" title="c23">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  or <font color="Maroon" title="c23">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E139">A109</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>;<br/><a NAME="E4:57_9_1_1_14_1_2_1_1_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E24:57_9_1_1"><span class="lab"><font color="Green" title="E108">A71</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_2_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E145">A115</font></span></a>, <a class="ref" href="jordan1g.html#T52" target="_self" title="JORDAN1G:th.52">Th60</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><span class="kw">hence </span><a NAME="E5:57_9_1_1_14_1_2_1_1_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E15:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E144">A114</font></span></a>, <a class="txt" href="#E11:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E142">A112</font></span></a>, <a class="txt" href="#E14:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E143">A113</font></span></a>, <a class="txt" href="#E9:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E141">A111</font></span></a>, <a class="txt" href="#E3:57_9_1_1_14_1_2_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E146">A116</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_2_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_2_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E145">A117</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="ref" href="finseq_4.html#T21" title="FINSEQ_4:th.21">FINSEQ_4:21</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c24">i</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E137">A107</font></span></a>, <a class="ref" href="topreal1.html#D3" title="TOPREAL1:def.3">TOPREAL1:def 3</a></span>;<br/><a NAME="E4:57_9_1_1_14_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
(  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  or  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E142">A112</font></span></a>, <a class="txt" href="#E14:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E143">A113</font></span></a>, <a class="ref" href="sppol_1.html#T19" title="SPPOL_1:th.19">SPPOL_1:19</a></span>;<br/><span class="kw">hence </span><a NAME="E5:57_9_1_1_14_1_2_1_1_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="txt" href="#E71:57"><span class="lab"><font color="Green" title="E89">A45</font></span></a>, <a class="txt" href="#E21:57_9_1_1"><span class="lab"><font color="Green" title="E106">A67</font></span></a>, <a class="txt" href="#E3:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E136">A106</font></span></a>, <a class="txt" href="#E7:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E139">A109</font></span></a>, <a class="txt" href="#E11:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E142">A112</font></span></a>, <a class="txt" href="#E9:57_9_1_1_14_1_2_1_1_2"><span class="lab"><font color="Green" title="E141">A111</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_2_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E145">A117</font></span></a>, <a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a>, <a class="ref" href="sppol_1.html#T40" title="SPPOL_1:th.40">SPPOL_1:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E17:57_9_1_1_14_1_2_1_1_2"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:57_9_1_1_14_1_2"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_3"/><span class="lab"><font color="Green" title="E134">A118</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E135">A119</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c23">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:57"><span class="lab"><font color="Green" title="E54">A8</font></span></a>, <a class="txt" href="#E55:57_9_1_1"><span class="lab"><font color="Green" title="E124">A87</font></span></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_3"/><span class="lab"><font color="Green" title="E136">A120</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:57_9_1_1"><span class="lab"><font color="Green" title="E127">A90</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_3"><span class="lab"><font color="Green" title="E134">A118</font></span></a>, <a class="ref" href="sppol_1.html#T41" title="SPPOL_1:th.41">SPPOL_1:41</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14_1_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1_3_1_1"/>
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:57_9_1_1"><span class="lab"><font color="Green" title="E129">A92</font></span></a>, <a class="txt" href="#E51:57_9_1_1"><span class="lab"><font color="Green" title="E122">A85</font></span></a>, <a class="txt" href="#E38:57_9_1_1"><span class="lab"><font color="Green" title="E115">A78</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_3_1_1_1"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:57_9_1_1_14_1_3_1_1_1"/><span class="lab"><font color="Green" title="E137">A121</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">i</font>
 <span class="kw">and </span><br/><a NAME="E4:57_9_1_1_14_1_3_1_1_1"/><span class="lab"><font color="Green" title="E138">A122</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:57_9_1_1_14_1_3_1_1_1"/><span class="lab"><font color="Green" title="E139">A123</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_2.html#T14" title="SPPOL_2:th.14">SPPOL_2:14</a></span>;<br/><a NAME="E6:57_9_1_1_14_1_3_1_1_1"/>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E7:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E140">A124</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E8:57_9_1_1_14_1_3_1_1_1"/>
<font color="Maroon" title="c24">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E138">A122</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E9:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E137">A121</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E141">A125</font></span>: <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font> = 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="txt" href="#E42:57_9_1_1"><span class="lab"><font color="Green" title="E117">A80</font></span></a>, <a class="ref" href="sprect_2.html#T3" title="SPRECT_2:th.3">SPRECT_2:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E140">A124</font></span></a>, <a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>
;<br/><a NAME="E11:57_9_1_1_14_1_3_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E12:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E142">A126</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E13:57_9_1_1_14_1_3_1_1_1"/><span class="lab"><font color="Green" title="E143">A127</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E14:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E138">A122</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E144">A128</font></span>: <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="txt" href="#E42:57_9_1_1"><span class="lab"><font color="Green" title="E117">A80</font></span></a>, <a class="ref" href="sprect_2.html#T3" title="SPRECT_2:th.3">SPRECT_2:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E142">A126</font></span></a>, <a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>
;<br/><a NAME="E16:57_9_1_1_14_1_3_1_1_1"/><span class="lab"><font color="Green" title="E145">A129</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:57_9_1_1"><span class="lab"><font color="Green" title="E118">A81</font></span></a>, <a class="txt" href="#E4:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E138">A122</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E17:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E18:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E146">A130</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E10:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E141">A125</font></span></a>, <a class="ref" href="jordan1g.html#T51" target="_self" title="JORDAN1G:th.51">Th59</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E19:57_9_1_1_14_1_3_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E16:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E145">A129</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E20:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E141">A125</font></span></a>, <a class="txt" href="#E13:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E143">A127</font></span></a>, <a class="txt" href="#E15:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E144">A128</font></span></a>, <a class="ref" href="topreal1.html#D3" title="TOPREAL1:def.3">TOPREAL1:def 3</a></span>;<br/><a NAME="E21:57_9_1_1_14_1_3_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E147">A131</font></span>: 
(  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  or  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T19" title="SPPOL_1:th.19">SPPOL_1:19</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1_1_3"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1_1_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_1_14_1_3_1_1_1_3_1"/>
( <font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E138">A122</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_3_1_1_1_3_1_1"/>
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_3_1_1_1_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E3:57_9_1_1_14_1_3_1_1_1_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:57_9_1_1"><span class="lab"><font color="Green" title="E118">A81</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E4:57_9_1_1_14_1_3_1_1_1_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E5:57_9_1_1_14_1_3_1_1_1_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E148">A132</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E15:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E144">A128</font></span></a>, <a class="ref" href="jordan1g.html#T51" target="_self" title="JORDAN1G:th.51">Th59</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E6:57_9_1_1_14_1_3_1_1_1_3_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  )
 ;<br/><span class="kw">hence </span><a NAME="E7:57_9_1_1_14_1_3_1_1_1_3_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="txt" href="#E3:57_9_1_1_14_1_3"><span class="lab"><font color="Green" title="E136">A120</font></span></a>, <a class="txt" href="#E5:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E139">A123</font></span></a>, <a class="txt" href="#E18:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E146">A130</font></span></a>, <a class="txt" href="#E5:57_9_1_1_14_1_3_1_1_1_3_1_1"><span class="lab"><font color="Green" title="E148">A132</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_3_1_1_1_3_1_2"/><span class="lab"><font color="Green" title="E148">A133</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_1_14_1_3_1_1_1_3_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c24">i</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E38:57_9_1_1"><span class="lab"><font color="Green" title="E115">A78</font></span></a>, <a class="txt" href="#E18:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E146">A130</font></span></a>, <a class="txt" href="#E21:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E147">A131</font></span></a>, <a class="ref" href="sppol_1.html#T15" title="SPPOL_1:th.15">SPPOL_1:15</a>, <a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a></span>;<br/><span class="kw">hence </span><a NAME="E3:57_9_1_1_14_1_3_1_1_1_3_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E87:57"><span class="lab"><font color="Green" title="E97">A53</font></span></a>, <a class="txt" href="#E38:57_9_1_1"><span class="lab"><font color="Green" title="E115">A78</font></span></a>, <a class="txt" href="#E2:57_9_1_1_14_1_3"><span class="lab"><font color="Green" title="E135">A119</font></span></a>, <a class="txt" href="#E5:57_9_1_1_14_1_3_1_1_1"><span class="lab"><font color="Green" title="E139">A123</font></span></a>, <a class="txt" href="#E1:57_9_1_1_14_1_3_1_1_1_3_1_2"><span class="lab"><font color="Green" title="E148">A133</font></span></a>, <a class="ref" href="goboard7.html#T6" title="GOBOARD7:th.6">GOBOARD7:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E23:57_9_1_1_14_1_3_1_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_1_14_1_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_1_14_1_3_1_1_2"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:57_9_1_1_14_1_3_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E87:57"><span class="lab"><font color="Green" title="E97">A53</font></span></a>, <a class="txt" href="#E57:57_9_1_1"><span class="lab"><font color="Green" title="E126">A89</font></span></a>, <a class="txt" href="#E2:57_9_1_1_14_1_3"><span class="lab"><font color="Green" title="E135">A119</font></span></a>, <a class="ref" href="sppol_1.html#T40" title="SPPOL_1:th.40">SPPOL_1:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:57_9_1_1_14_1_3"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E73:57_9_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2"/><span class="lab"><font color="Green" title="E99">A134</font></span>: 
 <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c18">RevLS</font> =  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> as   <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ;<br/><span class="kw">set </span><font color="Maroon" title="c19">h</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/><a NAME="E3:57_9_1_2"/><span class="lab"><font color="Green" title="E100">A135</font></span>: 
( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c18">RevLS</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T93" title="FINSEQ_3:th.93">FINSEQ_3:93</a></span>;<br/><a NAME="E4:57_9_1_2"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:57"><span class="lab"><font color="Green" title="E71">A25</font></span></a>, <a class="ref" href="zfmisc_1.html#T50" title="ZFMISC_1:th.50">ZFMISC_1:50</a></span>;<br/><a NAME="E5:57_9_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><a NAME="E6:57_9_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/><a NAME="E7:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A136</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T42" title="FINSEQ_5:th.42">FINSEQ_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T45" title="FINSEQ_5:th.45">FINSEQ_5:45</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>
;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">h</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>   <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57_9_1_2"><span class="lab"><font color="Green" title="E101">A136</font></span></a>, <a class="txt" href="#E3:57_9_1_2"><span class="lab"><font color="Green" title="E100">A135</font></span></a>, <a class="ref" href="finseq_3.html#T91" title="FINSEQ_3:th.91">FINSEQ_3:91</a>, <a class="ref" href="goboard2.html#T8" title="GOBOARD2:th.8">GOBOARD2:8</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c21">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> implies (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> ) )</span><br/><a NAME="E1:57_9_1_2_2"/><span class="lab"><font color="Green" title="E102">A138</font></span>: 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T21" title="SPRECT_1:th.21">SPRECT_1:21</a></span>;<br/><span class="kw">assume </span><a NAME="E2:57_9_1_2_2"/>
<font color="Maroon" title="c21">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E3:57_9_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c21">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>;<br/><a NAME="E4:57_9_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c21">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:57_9_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A139</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T16" title="FINSEQ_4:th.16">FINSEQ_4:16</a></span>;<br/><a NAME="E6:57_9_1_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E7:57_9_1_2_2"/>
(  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_2_2"><span class="lab"><font color="Green" title="E102">A138</font></span></a>, <a class="ref" href="jordan6.html#T1" title="JORDAN6:th.1">JORDAN6:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )</span><br/><a NAME="E8:57_9_1_2_2"/>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:57_9_1_2_2"><span class="lab"><font color="Green" title="E103">A139</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><span class="kw">hence </span><a NAME="E9:57_9_1_2_2"/>
(  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">m</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T22" title="SPRECT_1:th.22">SPRECT_1:22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E11:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A140</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</a></span>;<br/><a NAME="E12:57_9_1_2"/>
 <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T18" title="JORDAN1E:th.18">JORDAN1E:18</a>, <a class="ref" href="sprect_3.html#T51" title="SPRECT_3:th.51">SPRECT_3:51</a></span>;<br/><a NAME="E13:57_9_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="jordan1e.html#T1" title="JORDAN1E:th.1">JORDAN1E:1</a></span>;<br/><a NAME="E14:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A141</font></span>: 
<font color="Maroon" title="c20">h</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:57_9_1_2"><span class="lab"><font color="Green" title="E102">A140</font></span></a>, <a class="ref" href="sprect_2.html#T24" title="SPRECT_2:th.24">SPRECT_2:24</a></span>;<br/><a NAME="E15:57_9_1_2"/><span class="lab"><font color="Green" title="E104">A142</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T16" title="FINSEQ_2:th.16">FINSEQ_2:16</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A143</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c20">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">h</font></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T67" title="FINSEQ_4:th.67">FINSEQ_4:67</a></span>
<br/>.= 
 <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
;<br/><a NAME="E17:57_9_1_2"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="sppol_2.html#T24" title="SPPOL_2:th.24">SPPOL_2:24</a></span>;<br/><a NAME="E18:57_9_1_2"/><span class="kw">then </span>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E19:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A144</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_2.html#T22" title="SPPOL_2:th.22">SPPOL_2:22</a></span>;<br/><a NAME="E20:57_9_1_2"/><span class="lab"><font color="Green" title="E107">A145</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:57"><span class="lab"><font color="Green" title="E66">A20</font></span></a>, <a class="ref" href="pscomp_1.html#T24" title="PSCOMP_1:th.24">PSCOMP_1:24</a></span>;<br/><a NAME="E21:57_9_1_2"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:57"><span class="lab"><font color="Green" title="E74">A28</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E22:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A146</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T42" title="FINSEQ_5:th.42">FINSEQ_5:42</a></span>;<br/><a NAME="E23:57_9_1_2"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c20">h</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></span>;<br/><a NAME="E24:57_9_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c20">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c20">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:57_9_1_2"><span class="lab"><font color="Green" title="E108">A146</font></span></a>, <a class="ref" href="finseq_6.html#T109" title="FINSEQ_6:th.109">FINSEQ_6:109</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T44" title="FINSEQ_5:th.44">FINSEQ_5:44</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T65" title="FINSEQ_5:th.65">FINSEQ_5:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T8" title="JORDAN1F:th.8">JORDAN1F:8</a></span>
<br/>.= 
 <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_2"><span class="lab"><font color="Green" title="E99">A134</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>
;<br/><a NAME="E26:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A147</font></span>: 
<font color="Maroon" title="c20">h</font> <a href="sprect_2.html#R3" title="SPRECT_2:pred.3">is_a_v.c._for</a>  <a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:57_9_1_2"><span class="lab"><font color="Green" title="E103">A141</font></span></a>, <a class="txt" href="#E16:57_9_1_2"><span class="lab"><font color="Green" title="E105">A143</font></span></a>, <a class="ref" href="sprect_2.html#D3" title="SPRECT_2:def.3">SPRECT_2:def 3</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c21">FiP2</font> =  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c22">midU</font> =  <a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>);<br/><a NAME="E27:57_9_1_2"/><span class="lab"><font color="Green" title="E110">A148</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><a NAME="E28:57_9_1_2"/><span class="lab"><font color="Green" title="E111">A149</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c17">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sppol_2.html#T19" title="SPPOL_2:th.19">SPPOL_2:19</a>, <a class="ref" href="sprect_2.html#T7" title="SPRECT_2:th.7">SPRECT_2:7</a></span>;<br/><a NAME="E29:57_9_1_2"/><span class="lab"><font color="Green" title="E112">A150</font></span>: 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="finseq_6.html#T42" title="FINSEQ_6:th.42">FINSEQ_6:42</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_5"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:57_9_1_2_5"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_6.html#T43" title="FINSEQ_6:th.43">FINSEQ_6:43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1f.html#T5" title="JORDAN1F:th.5">JORDAN1F:5</a></span>
;<br/><a NAME="E3:57_9_1_2_5"/><span class="kw">then </span>
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="txt" href="#E29:57_9_1_2"><span class="lab"><font color="Green" title="E112">A150</font></span></a>, <a class="ref" href="finseq_5.html#T9" title="FINSEQ_5:th.9">FINSEQ_5:9</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_9_1_2_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E31:57_9_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E32:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A151</font></span>: 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E33:57_9_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T19" title="XREAL_1:th.19">XREAL_1:19</a></span>;<br/><a NAME="E34:57_9_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E114">A152</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E32:57_9_1_2"><span class="lab"><font color="Green" title="E113">A151</font></span></a>, <a class="ref" href="jordan4.html#T8" title="JORDAN4:th.8">JORDAN4:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>

;<br/><a NAME="E36:57_9_1_2"/>
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><a NAME="E37:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E115">A153</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a></span>;<br/><a NAME="E38:57_9_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T16" title="FINSEQ_2:th.16">FINSEQ_2:16</a></span>;<br/><a NAME="E39:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A154</font></span>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E82:57"><span class="lab"><font color="Green" title="E95">A51</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><span class="lab"><font color="Green" title="E117">A155</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T42" title="FINSEQ_5:th.42">FINSEQ_5:42</a></span>
<br/>.= 
 <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T45" title="FINSEQ_5:th.45">FINSEQ_5:45</a></span>
;<br/><a NAME="E41:57_9_1_2"/>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:57_9_1_2"><span class="lab"><font color="Green" title="E108">A146</font></span></a>, <a class="txt" href="#E15:57_9_1_2"><span class="lab"><font color="Green" title="E104">A142</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E42:57_9_1_2"/><span class="kw">then </span>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c17">g</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c20">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E85:57"><span class="lab"><font color="Green" title="E96">A52</font></span></a>, <a class="txt" href="#E26:57_9_1_2"><span class="lab"><font color="Green" title="E109">A147</font></span></a>, <a class="txt" href="#E39:57_9_1_2"><span class="lab"><font color="Green" title="E116">A154</font></span></a>, <a class="ref" href="sprect_2.html#T29" title="SPRECT_2:th.29">SPRECT_2:29</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E44:57_9_1_2"/><span class="lab"><font color="Green" title="E118">A156</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c17">g</font>
 <span class="kw">and </span><br/><a NAME="E45:57_9_1_2"/><span class="lab"><font color="Green" title="E119">A157</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c20">h</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">x</font> = <font color="Maroon" title="c23">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:57_9_1_2"><span class="lab"><font color="Green" title="E118">A156</font></span></a></span>;<br/><a NAME="E47:57_9_1_2"/><span class="lab"><font color="Green" title="E120">A158</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c20">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p4">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p5">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T47" title="FINSEQ_5:th.47">FINSEQ_5:47</a>, <a class="ref" href="sppol_2.html#T19" title="SPPOL_2:th.19">SPPOL_2:19</a></span>;<br/><span class="lab"><font color="Green" title="E121">A159</font></span>: <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_2.html#T9" title="SPRECT_2:th.9">SPRECT_2:9</a></span>
<br/>.= 
 <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>
;<br/><a NAME="E49:57_9_1_2"/><span class="lab"><font color="Green" title="E122">A160</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="ref" href="sprect_3.html#T18" title="SPRECT_3:th.18">SPRECT_3:18</a></span>;<br/><a NAME="E50:57_9_1_2"/><span class="lab"><font color="Green" title="E123">A161</font></span>: 
(  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> &amp;  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:57"><span class="lab"><font color="Green" title="E58">A12</font></span></a>, <a class="txt" href="#E21:57"><span class="lab"><font color="Green" title="E63">A17</font></span></a>, <a class="ref" href="jordan5c.html#T18" title="JORDAN5C:th.18">JORDAN5C:18</a>, <a class="ref" href="sppol_2.html#T22" title="SPPOL_2:th.22">SPPOL_2:22</a></span>;<br/><a NAME="E51:57_9_1_2"/><span class="lab"><font color="Green" title="E124">A162</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/><a NAME="E52:57_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E125">A163</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T15" title="SPPOL_1:th.15">SPPOL_1:15</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_9"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_2_9_1"/>
( <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:57_9_1_2"><span class="lab"><font color="Green" title="E119">A157</font></span></a>, <a class="txt" href="#E47:57_9_1_2"><span class="lab"><font color="Green" title="E120">A158</font></span></a>, <a class="txt" href="#E40:57_9_1_2"><span class="lab"><font color="Green" title="E117">A155</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1"/><span class="lab"><font color="Green" title="E126">A164</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_9_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_2_9_1_1_1_1"/>
( <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:57_9_1_2"><span class="lab"><font color="Green" title="E118">A156</font></span></a>, <a class="txt" href="#E28:57_9_1_2"><span class="lab"><font color="Green" title="E111">A149</font></span></a>, <a class="txt" href="#E48:57_9_1_2"><span class="lab"><font color="Green" title="E121">A159</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1_1_1_1"/><span class="lab"><font color="Green" title="E127">A165</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:57_9_1_2"><span class="lab"><font color="Green" title="E122">A160</font></span></a>, <a class="txt" href="#E19:57_9_1_2"><span class="lab"><font color="Green" title="E106">A144</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_1"><span class="lab"><font color="Green" title="E126">A164</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E128">A166</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T16" title="JORDAN1E:th.16">JORDAN1E:16</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_2_9_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_9_1_2_9_1_1_1_1_1"><span class="lab"><font color="Green" title="E128">A166</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_1_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:57"><span class="lab"><font color="Green" title="E90">A46</font></span></a>, <a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_1_1_1_1"><span class="lab"><font color="Green" title="E127">A165</font></span></a>, <a class="ref" href="jordan1g.html#T37" target="_self" title="JORDAN1G:th.37">Th45</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_1_1_1_1_1_1_1"/><span class="kw">then </span>
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_9_1_2_9_1_1_1_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:57"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:57"><span class="lab"><font color="Green" title="E90">A46</font></span></a>, <a class="txt" href="#E51:57"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="txt" href="#E29:57"><span class="lab"><font color="Green" title="E70">A24</font></span></a>, <a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_1_1_1_1"><span class="lab"><font color="Green" title="E127">A165</font></span></a>, <a class="ref" href="jordan1g.html#T38" target="_self" title="JORDAN1G:th.38">Th46</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
 <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:57"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="txt" href="#E27:57"><span class="lab"><font color="Green" title="E68">A22</font></span></a>, <a class="ref" href="finseq_5.html#T38" title="FINSEQ_5:th.38">FINSEQ_5:38</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_9_1_2_9_1_1_1_1_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:57_9_1_2_9_1_1_1_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1_1_1_2"/><span class="lab"><font color="Green" title="E127">A167</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_1_1_1_2"/>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:57_9_1_2"><span class="lab"><font color="Green" title="E124">A162</font></span></a>, <a class="ref" href="sppol_1.html#T15" title="SPPOL_1:th.15">SPPOL_1:15</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E128">A168</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E127">A167</font></span></a>, <a class="ref" href="sppol_1.html#T40" title="SPPOL_1:th.40">SPPOL_1:40</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c25">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E5:57_9_1_2_9_1_1_1_1_2"/><span class="lab"><font color="Green" title="E129">A169</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c25">i</font>
 <span class="kw">and </span><br/><a NAME="E6:57_9_1_2_9_1_1_1_1_2"/><span class="lab"><font color="Green" title="E130">A170</font></span>: 
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:57_9_1_2_9_1_1_1_1_2"/><span class="lab"><font color="Green" title="E131">A171</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_9_1_2_9_1_1"><span class="lab"><font color="Green" title="E126">A164</font></span></a>, <a class="ref" href="sppol_2.html#T14" title="SPPOL_2:th.14">SPPOL_2:14</a></span>;<br/><a NAME="E8:57_9_1_2_9_1_1_1_1_2"/><span class="lab"><font color="Green" title="E132">A172</font></span>: 
<font color="Maroon" title="c25">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E130">A170</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E9:57_9_1_2_9_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E133">A173</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E50:57_9_1_2"><span class="lab"><font color="Green" title="E123">A161</font></span></a>, <a class="txt" href="#E5:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E129">A169</font></span></a>, <a class="ref" href="jordan1g.html#T52" target="_self" title="JORDAN1G:th.52">Th60</a></span>;<br/><a NAME="E10:57_9_1_2_9_1_1_1_1_2"/>
<font color="Maroon" title="c25">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E5:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E129">A169</font></span></a>, <a class="txt" href="#E8:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E132">A172</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E11:57_9_1_2_9_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E134">A174</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T43" title="FINSEQ_5:th.43">FINSEQ_5:43</a></span>;<br/><a NAME="E12:57_9_1_2_9_1_1_1_1_2"/>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E13:57_9_1_2_9_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E6:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E130">A170</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E14:57_9_1_2_9_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E135">A175</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="ref" href="finseq_5.html#T43" title="FINSEQ_5:th.43">FINSEQ_5:43</a></span>;<br/><a NAME="E15:57_9_1_2_9_1_1_1_1_2"/><span class="lab"><font color="Green" title="E136">A176</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:57"><span class="lab"><font color="Green" title="E78">A32</font></span></a>, <a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E27:57_9_1_2"><span class="lab"><font color="Green" title="E110">A148</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E127">A167</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_2_9_1_1_1_1_2_1_1"/>
( <font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> or <font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E130">A170</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E137">A177</font></span>: 
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_1_1_1_2_1_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  )
 ;<br/><a NAME="E3:57_9_1_2_9_1_1_1_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E138">A178</font></span>: 
( <font color="Maroon" title="c24">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  or <font color="Maroon" title="c24">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E131">A171</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>;<br/><a NAME="E4:57_9_1_2_9_1_1_1_1_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="txt" href="#E50:57_9_1_2"><span class="lab"><font color="Green" title="E123">A161</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E137">A177</font></span></a>, <a class="ref" href="jordan1g.html#T52" target="_self" title="JORDAN1G:th.52">Th60</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><span class="kw">hence </span><a NAME="E5:57_9_1_2_9_1_1_1_1_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E15:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E136">A176</font></span></a>, <a class="txt" href="#E11:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E134">A174</font></span></a>, <a class="txt" href="#E14:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E135">A175</font></span></a>, <a class="txt" href="#E9:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E133">A173</font></span></a>, <a class="txt" href="#E3:57_9_1_2_9_1_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E138">A178</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_1_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_1_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E137">A179</font></span>: 
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_1_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:57"><span class="lab"><font color="Green" title="E73">A27</font></span></a>, <a class="txt" href="#E50:57"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <a class="ref" href="finseq_4.html#T21" title="FINSEQ_4:th.21">FINSEQ_4:21</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_1_1_1_2_1_1_2"/><span class="kw">then </span>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c25">i</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E129">A169</font></span></a>, <a class="ref" href="topreal1.html#D3" title="TOPREAL1:def.3">TOPREAL1:def 3</a></span>;<br/><a NAME="E4:57_9_1_2_9_1_1_1_1_2_1_1_2"/><span class="kw">then </span>
(  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  or  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E134">A174</font></span></a>, <a class="txt" href="#E14:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E135">A175</font></span></a>, <a class="ref" href="sppol_1.html#T19" title="SPPOL_1:th.19">SPPOL_1:19</a></span>;<br/><span class="kw">hence </span><a NAME="E5:57_9_1_2_9_1_1_1_1_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="txt" href="#E71:57"><span class="lab"><font color="Green" title="E89">A45</font></span></a>, <a class="txt" href="#E40:57_9_1_2"><span class="lab"><font color="Green" title="E117">A155</font></span></a>, <a class="txt" href="#E3:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E128">A168</font></span></a>, <a class="txt" href="#E7:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E131">A171</font></span></a>, <a class="txt" href="#E11:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E134">A174</font></span></a>, <a class="txt" href="#E9:57_9_1_2_9_1_1_1_1_2"><span class="lab"><font color="Green" title="E133">A173</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E137">A179</font></span></a>, <a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a>, <a class="ref" href="sppol_1.html#T40" title="SPPOL_1:th.40">SPPOL_1:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E17:57_9_1_2_9_1_1_1_1_2"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:57_9_1_2_9_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_2"/><span class="lab"><font color="Green" title="E126">A180</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E127">A181</font></span>: 
<span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:57"><span class="lab"><font color="Green" title="E54">A8</font></span></a>, <a class="txt" href="#E20:57_9_1_2"><span class="lab"><font color="Green" title="E107">A145</font></span></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_2"/><span class="lab"><font color="Green" title="E128">A182</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K2" title="JORDAN5C:func.2">Last_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:57_9_1_2"><span class="lab"><font color="Green" title="E115">A153</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_2"><span class="lab"><font color="Green" title="E126">A180</font></span></a>, <a class="ref" href="sppol_1.html#T41" title="SPPOL_1:th.41">SPPOL_1:41</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_9_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_2_9_1_2_1_1"/>
( <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:57_9_1_2"><span class="lab"><font color="Green" title="E118">A156</font></span></a>, <a class="txt" href="#E28:57_9_1_2"><span class="lab"><font color="Green" title="E111">A149</font></span></a>, <a class="txt" href="#E48:57_9_1_2"><span class="lab"><font color="Green" title="E121">A159</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_2_1_1_1"/>
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:57_9_1_2_9_1_2_1_1_1"/><span class="lab"><font color="Green" title="E129">A183</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c25">i</font>
 <span class="kw">and </span><br/><a NAME="E4:57_9_1_2_9_1_2_1_1_1"/><span class="lab"><font color="Green" title="E130">A184</font></span>: 
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:57_9_1_2_9_1_2_1_1_1"/><span class="lab"><font color="Green" title="E131">A185</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_2.html#T14" title="SPPOL_2:th.14">SPPOL_2:14</a></span>;<br/><a NAME="E6:57_9_1_2_9_1_2_1_1_1"/>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E7:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E132">A186</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E8:57_9_1_2_9_1_2_1_1_1"/>
<font color="Maroon" title="c25">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E130">A184</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E9:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E129">A183</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E133">A187</font></span>: <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font> = 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="txt" href="#E32:57_9_1_2"><span class="lab"><font color="Green" title="E113">A151</font></span></a>, <a class="ref" href="sprect_2.html#T3" title="SPRECT_2:th.3">SPRECT_2:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E132">A186</font></span></a>, <a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>
;<br/><a NAME="E11:57_9_1_2_9_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E12:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E134">A188</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E13:57_9_1_2_9_1_2_1_1_1"/><span class="lab"><font color="Green" title="E135">A189</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E14:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E130">A184</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E136">A190</font></span>: <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:57"><span class="lab"><font color="Green" title="E91">A47</font></span></a>, <a class="txt" href="#E28:57"><span class="lab"><font color="Green" title="E69">A23</font></span></a>, <a class="txt" href="#E32:57_9_1_2"><span class="lab"><font color="Green" title="E113">A151</font></span></a>, <a class="ref" href="sprect_2.html#T3" title="SPRECT_2:th.3">SPRECT_2:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E134">A188</font></span></a>, <a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>
;<br/><a NAME="E16:57_9_1_2_9_1_2_1_1_1"/><span class="lab"><font color="Green" title="E137">A191</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:57_9_1_2"><span class="lab"><font color="Green" title="E114">A152</font></span></a>, <a class="txt" href="#E4:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E130">A184</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E17:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E18:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E138">A192</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E10:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E133">A187</font></span></a>, <a class="ref" href="jordan1g.html#T51" target="_self" title="JORDAN1G:th.51">Th59</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E19:57_9_1_2_9_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E68:57"><span class="lab"><font color="Green" title="E87">A43</font></span></a>, <a class="txt" href="#E16:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E137">A191</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E20:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E133">A187</font></span></a>, <a class="txt" href="#E13:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E135">A189</font></span></a>, <a class="txt" href="#E15:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E136">A190</font></span></a>, <a class="ref" href="topreal1.html#D3" title="TOPREAL1:def.3">TOPREAL1:def 3</a></span>;<br/><a NAME="E21:57_9_1_2_9_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E139">A193</font></span>: 
(  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  or  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>) is  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T19" title="SPPOL_1:th.19">SPPOL_1:19</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1_1_3"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1_1_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_9_1_2_9_1_2_1_1_1_3_1"/>
( <font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> or <font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E130">A184</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_2_1_1_1_3_1_1"/>
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_2_1_1_1_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E3:57_9_1_2_9_1_2_1_1_1_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:57_9_1_2"><span class="lab"><font color="Green" title="E114">A152</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E4:57_9_1_2_9_1_2_1_1_1_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E5:57_9_1_2_9_1_2_1_1_1_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E140">A194</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:57"><span class="lab"><font color="Green" title="E67">A21</font></span></a>, <a class="txt" href="#E15:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E136">A190</font></span></a>, <a class="ref" href="jordan1g.html#T51" target="_self" title="JORDAN1G:th.51">Th59</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E6:57_9_1_2_9_1_2_1_1_1_3_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  )
 ;<br/><span class="kw">hence </span><a NAME="E7:57_9_1_2_9_1_2_1_1_1_3_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:57"><span class="lab"><font color="Green" title="E88">A44</font></span></a>, <a class="txt" href="#E3:57_9_1_2_9_1_2"><span class="lab"><font color="Green" title="E128">A182</font></span></a>, <a class="txt" href="#E5:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E131">A185</font></span></a>, <a class="txt" href="#E18:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E138">A192</font></span></a>, <a class="txt" href="#E5:57_9_1_2_9_1_2_1_1_1_3_1_1"><span class="lab"><font color="Green" title="E140">A194</font></span></a>, <a class="ref" href="topreal1.html#T3" title="TOPREAL1:th.3">TOPREAL1:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_2_1_1_1_3_1_2"/><span class="lab"><font color="Green" title="E140">A195</font></span>: 
<font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:57_9_1_2_9_1_2_1_1_1_3_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c25">i</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p4">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E64:57"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E48:57_9_1_2"><span class="lab"><font color="Green" title="E121">A159</font></span></a>, <a class="txt" href="#E18:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E138">A192</font></span></a>, <a class="txt" href="#E21:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E139">A193</font></span></a>, <a class="ref" href="sppol_1.html#T15" title="SPPOL_1:th.15">SPPOL_1:15</a>, <a class="ref" href="sppol_1.html#T16" title="SPPOL_1:th.16">SPPOL_1:16</a></span>;<br/><span class="kw">hence </span><a NAME="E3:57_9_1_2_9_1_2_1_1_1_3_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E87:57"><span class="lab"><font color="Green" title="E97">A53</font></span></a>, <a class="txt" href="#E48:57_9_1_2"><span class="lab"><font color="Green" title="E121">A159</font></span></a>, <a class="txt" href="#E2:57_9_1_2_9_1_2"><span class="lab"><font color="Green" title="E127">A181</font></span></a>, <a class="txt" href="#E5:57_9_1_2_9_1_2_1_1_1"><span class="lab"><font color="Green" title="E131">A185</font></span></a>, <a class="txt" href="#E1:57_9_1_2_9_1_2_1_1_1_3_1_2"><span class="lab"><font color="Green" title="E140">A195</font></span></a>, <a class="ref" href="goboard7.html#T6" title="GOBOARD7:th.6">GOBOARD7:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E23:57_9_1_2_9_1_2_1_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_9_1_2_9_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_9_1_2_9_1_2_1_1_2"/>
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p0">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan5c.html#K1" title="JORDAN5C:func.1">First_Point</a> (<span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p5">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p0">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:57_9_1_2_9_1_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E87:57"><span class="lab"><font color="Green" title="E97">A53</font></span></a>, <a class="txt" href="#E52:57_9_1_2"><span class="lab"><font color="Green" title="E125">A163</font></span></a>, <a class="txt" href="#E2:57_9_1_2_9_1_2"><span class="lab"><font color="Green" title="E127">A181</font></span></a>, <a class="ref" href="sppol_1.html#T40" title="SPPOL_1:th.40">SPPOL_1:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:57_9_1_2_9_1_2"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E54:57_9_1_2"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E90:57"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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