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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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>  st 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c1">n</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="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <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="Olive" title="b1">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c4">b</font> <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="Olive" title="b1">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> holds <br/><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="Olive" title="b1">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">n</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="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Olive" title="b1">D</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</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="c5">D</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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="Red">::  thesis: </font></span></a><span class="hide"> ( 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c1">n</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="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <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="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c4">b</font> <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="c5">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> implies <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="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">n</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="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</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="c6">I</font> =  <a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c2">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">J</font> =  <a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">z</font> =  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <font color="Maroon" title="c5">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">e</font> =  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <font color="Maroon" title="c5">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">s</font> =  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">w</font> =  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c5">D</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">and </span><br/><a NAME="E2:22"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c1">n</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="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:22"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E4:22"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<font color="Maroon" title="c3">a</font> <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="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:22"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E6:22"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<font color="Maroon" title="c4">b</font> <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="c5">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">n</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="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> </span><br/>

<a NAME="E7:22"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>;<br/>
<a NAME="E8:22"/><span class="kw">then </span>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="jordan1d.html#E21"><span class="lab"><font color="Green" title="E15">Lm13</font></span></a></span>;<br/>
<a NAME="E9:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A7</font></span>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2 <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="c5">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">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="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>;<br/>
<a NAME="E10:22"/><span class="lab"><font color="Green" title="E26">A8</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="c5">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">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="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="c5">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">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="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>;<br/>
<a NAME="E11:22"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="jordan1d.html#E19"><span class="lab"><font color="Green" title="E13">Lm11</font></span></a></span>;<br/>
<a NAME="E12:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">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="#E5:22"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="matrix_1.html#T37" title="MATRIX_1:th.37">MATRIX_1:37</a></span>;<br/>
<a NAME="E13:22"/><span class="lab"><font color="Green" title="E28">A10</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="c5">D</font>,<font color="Maroon" title="c2">i</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="c5">D</font>,<font color="Maroon" title="c2">i</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="E14:22"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E15:22"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">n</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E13:22"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="matrix_1.html#T37" title="MATRIX_1:th.37">MATRIX_1:37</a></span>;<br/>
<span class="kw">hence </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="c5">D</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">n</font></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"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<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#K8" title="PSCOMP_1:func.8">E-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<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#K7" title="PSCOMP_1:func.7">N-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</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="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <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="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <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="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="jordan1d.html#E18"><span class="lab"><font color="Green" title="E12">Lm10</font></span></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"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<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#K8" title="PSCOMP_1:func.8">E-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<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#K7" title="PSCOMP_1:func.7">N-bound</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</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="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>
<br/>.= 
<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="c5">D</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</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="#E12:22"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="jordan8.html#D1" title="JORDAN8:def.1">JORDAN8:def 1</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
