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<span class="kw">let </span><font color="Maroon" title="c22">C</font> be   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="jordan24.html#R1" title="JORDAN24:pred.1">realize-max-dist-in</a> <font color="Maroon" title="c22">C</font> implies  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c22">C</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:145"/><span class="lab"><font color="Green" title="E176">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="jordan24.html#R1" title="JORDAN24:pred.1">realize-max-dist-in</a> <font color="Maroon" title="c22">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c22">C</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c23">Jc</font> =  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c22">C</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c24">Pf</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c25">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:145"/><span class="lab"><font color="Green" title="E177">A2</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c25">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 <span class="kw">and </span><br/><a NAME="E4:145"/><span class="lab"><font color="Green" title="E178">A3</font></span>: 
<font color="Maroon" title="c24">Pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan.html#T43" target="_self" title="JORDAN:th.43">Th43</a></span>;<br/>
<a NAME="E5:145"/><span class="lab"><font color="Green" title="E179">A4</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="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></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> <font color="Maroon" title="c22">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:145"><span class="lab"><font color="Green" title="E176">A1</font></span></a>, <a class="ref" href="jordan.html#T79" target="_self" title="JORDAN:th.79">Th79</a></span>;<br/>
<a NAME="E6:145"/>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></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> <font color="Maroon" title="c22">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:145"><span class="lab"><font color="Green" title="E176">A1</font></span></a>, <a class="ref" href="jordan.html#T80" target="_self" title="JORDAN:th.80">Th80</a></span>;<br/>
<a NAME="E7:145"/><span class="kw">then </span>
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c22">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</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="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:145"><span class="lab"><font color="Green" title="E179">A4</font></span></a>, <a class="ref" href="jordan6.html#D8" title="JORDAN6:def.8">JORDAN6:def 8</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">Pg</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c27">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c22">C</font></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E9:145"/><span class="lab"><font color="Green" title="E180">A5</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c27">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">and </span><br/><a NAME="E10:145"/><span class="lab"><font color="Green" title="E181">A6</font></span>: 
<font color="Maroon" title="c26">Pg</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c27">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan.html#T42" target="_self" title="JORDAN:th.42">Th42</a></span>;<br/>
<a NAME="E11:145"/><span class="lab"><font color="Green" title="E182">A7</font></span>: 
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c22">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c22">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan6.html#T76" title="JORDAN6:th.76">JORDAN6:76</a></span>;<br/>
<a NAME="E12:145"/><span class="lab"><font color="Green" title="E183">A8</font></span>: 
<font color="Maroon" title="c22">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span>,3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:145"><span class="lab"><font color="Green" title="E176">A1</font></span></a>, <a class="ref" href="jordan.html#T71" target="_self" title="JORDAN:th.71">Th71</a></span>;<br/>
<a NAME="E13:145"/><span class="lab"><font color="Green" title="E184">A9</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="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:145"><span class="lab"><font color="Green" title="E176">A1</font></span></a>, <a class="ref" href="jordan24.html#D1" title="JORDAN24:def.1">JORDAN24:def 1</a></span>;<br/>
<a NAME="E14:145"/><span class="lab"><font color="Green" title="E185">A10</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:145"><span class="lab"><font color="Green" title="E176">A1</font></span></a>, <a class="ref" href="jordan24.html#D1" title="JORDAN24:def.1">JORDAN24:def 1</a></span>;<br/>
<a NAME="E15:145"/><span class="lab"><font color="Green" title="E186">A11</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topreala.html#K1" title="TOPREALA:func.1">Trectangle</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span>,3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span>,3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c28">AR</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c29">BR</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c30">CR</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c31">DR</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="topreala.html#K1" title="TOPREALA:func.1">Trectangle</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span>,3</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:145"><span class="lab"><font color="Green" title="E183">A8</font></span></a>, <a class="txt" href="#E13:145"><span class="lab"><font color="Green" title="E184">A9</font></span></a>, <a class="txt" href="#E14:145"><span class="lab"><font color="Green" title="E185">A10</font></span></a>, <a class="txt" href="jordan.html#E143"><span class="lab"><font color="Green" title="E125">Lm62</font></span></a>, <a class="txt" href="jordan.html#E144"><span class="lab"><font color="Green" title="E126">Lm63</font></span></a>, <a class="txt" href="jordan.html#E150"><span class="lab"><font color="Green" title="E132">Lm67</font></span></a>, <a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></span>;<br/>
<a NAME="E17:145"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c26">Pg</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topreala.html#K1" title="TOPREALA:func.1">Trectangle</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span>,3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:145"><span class="lab"><font color="Green" title="E180">A5</font></span></a>, <a class="txt" href="#E10:145"><span class="lab"><font color="Green" title="E181">A6</font></span></a>, <a class="txt" href="#E11:145"><span class="lab"><font color="Green" title="E182">A7</font></span></a>, <a class="txt" href="#E12:145"><span class="lab"><font color="Green" title="E183">A8</font></span></a>, <a class="txt" href="#E15:145"><span class="lab"><font color="Green" title="E186">A11</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c32">h</font> = <font color="Maroon" title="c26">Pg</font> as    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c28">AR</font>,<font color="Maroon" title="c29">BR</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan.html#T30" target="_self" title="JORDAN:th.30">Th30</a></span>;<br/>
<a NAME="E19:145"/>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span>,3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="jordan.html#E143"><span class="lab"><font color="Green" title="E125">Lm62</font></span></a>, <a class="txt" href="jordan.html#E144"><span class="lab"><font color="Green" title="E126">Lm63</font></span></a>, <a class="txt" href="jordan.html#E150"><span class="lab"><font color="Green" title="E132">Lm67</font></span></a>, <a class="ref" href="jordan1.html#D1" title="JORDAN1:def.1">JORDAN1:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c33">v</font> = <font color="Maroon" title="c24">Pf</font> as    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c30">CR</font>,<font color="Maroon" title="c31">DR</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:145"><span class="lab"><font color="Green" title="E177">A2</font></span></a>, <a class="txt" href="#E4:145"><span class="lab"><font color="Green" title="E178">A3</font></span></a>, <a class="txt" href="#E15:145"><span class="lab"><font color="Green" title="E186">A11</font></span></a>, <a class="ref" href="jordan.html#T30" target="_self" title="JORDAN:th.30">Th30</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c34">s</font>, <font color="Maroon" title="c35">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw"> such that </span><br/><a NAME="E22:145"/><span class="lab"><font color="Green" title="E187">A12</font></span>: 
<font color="Maroon" title="c32">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c35">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="jordan.html#E93"><span class="lab"><font color="Green" title="E79">Lm16</font></span></a>, <a class="txt" href="jordan.html#E94"><span class="lab"><font color="Green" title="E80">Lm17</font></span></a>, <a class="txt" href="jordan.html#E98"><span class="lab"><font color="Green" title="E84">Lm21</font></span></a>, <a class="txt" href="jordan.html#E100"><span class="lab"><font color="Green" title="E86">Lm23</font></span></a>, <a class="ref" href="jgraph_8.html#T6" title="JGRAPH_8:th.6">JGRAPH_8:6</a></span>;<br/>
<a NAME="E23:145"/><span class="lab"><font color="Green" title="E188">A13</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c32">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E24:145"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c33">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E25:145"/><span class="kw">then </span><span class="lab"><font color="Green" title="E189">A14</font></span>: 
<font color="Maroon" title="c33">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c35">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c24">Pf</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E26:145"/>
<font color="Maroon" title="c32">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c26">Pg</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:145"><span class="lab"><font color="Green" title="E188">A13</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:145"/>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,3</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 3</span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:145"><span class="lab"><font color="Green" title="E177">A2</font></span></a>, <a class="txt" href="#E4:145"><span class="lab"><font color="Green" title="E178">A3</font></span></a>, <a class="txt" href="#E9:145"><span class="lab"><font color="Green" title="E180">A5</font></span></a>, <a class="txt" href="#E10:145"><span class="lab"><font color="Green" title="E181">A6</font></span></a>, <a class="txt" href="#E11:145"><span class="lab"><font color="Green" title="E182">A7</font></span></a>, <a class="txt" href="#E22:145"><span class="lab"><font color="Green" title="E187">A12</font></span></a>, <a class="txt" href="#E25:145"><span class="lab"><font color="Green" title="E189">A14</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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