<?xml version="1.0"?>
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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">W</font> is <a href="chord.html#V1" target="_self">minlength</a>
 ;<br/>

<b>assume </b><a NAME="E2:42"/>
not <font color="Maroon">W</font> is <a href="glib_001.html#V5">Path-like</a>
 ;<br/>

<b>then consider </b><font color="Maroon">m</font> being  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> being  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:42"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> )
 <b>and </b><br/><a NAME="E5:42"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E6:42"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="glib_001.html#T147">GLIB_001:147</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1"/>
( <font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font> or <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> )
 </span><b>by </b><i><a class="ref" href="chord.html#T3" target="_self">Th3</a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1"><b>suppose </b></a><a NAME="E1:42_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">R</font> = <font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font>;<br/><b>set </b><font color="Maroon">S</font> = <font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span>;<br/><a NAME="E2:42_1_1"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><a NAME="E3:42_1_1"/><b>then </b><i><font color="Green">E67</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> )
 <b>by </b><i>, <a class="ref" href="glib_001.html#T38">GLIB_001:38</a></i>;<br/><a NAME="E4:42_1_1"/><i><font color="Green">E68</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="glib_001.html#T38">GLIB_001:38</a></i>;<br/><a NAME="E5:42_1_1"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="chord.html#T4" target="_self">Th4</a>, , <a class="ref" href="glib_001.html#T37">GLIB_001:37</a></i>;<br/><a NAME="E6:42_1_1"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="glib_001.html#T37">GLIB_001:37</a></i>;<br/><b>set </b><font color="Maroon">P</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span>;<br/><a NAME="E7:42_1_1"/><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">W</font> <a href="glib_001.html#K3">.first()</a> ,<font color="Maroon">W</font> <a href="glib_001.html#K4">.last()</a> 
 <b>by </b><i><a class="ref" href="chord.html#T5" target="_self">Th5</a>, <a class="ref" href="chord.html#T6" target="_self">Th6</a>, <a class="ref" href="glib_001.html#T31">GLIB_001:31</a></i>;<br/><a NAME="E8:42_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="chord.html#T5" target="_self">Th5</a>, <a class="ref" href="chord.html#T6" target="_self">Th6</a>, <a class="ref" href="glib_001.html#T29">GLIB_001:29</a></i>;<br/><a NAME="E9:42_1_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="chord.html#T7" target="_self">Th7</a>, <a class="ref" href="chord.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:42_1_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">m</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">n</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E11:42_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="chord.html#T10" target="_self">Th10</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_2"><b>suppose </b></a><a NAME="E1:42_1_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">R</font> = <font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font>;<br/><b>set </b><font color="Maroon">S</font> = <font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span>;<br/><a NAME="E2:42_1_2"/><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><a NAME="E3:42_1_2"/><b>then </b><i><font color="Green">E74</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>by </b><i>, <a class="ref" href="glib_001.html#T38">GLIB_001:38</a></i>;<br/><a NAME="E4:42_1_2"/><i><font color="Green">E75</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="glib_001.html#T38">GLIB_001:38</a></i>;<br/><a NAME="E5:42_1_2"/><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="chord.html#T4" target="_self">Th4</a>, , <a class="ref" href="glib_001.html#T37">GLIB_001:37</a></i>;<br/><a NAME="E6:42_1_2"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font>
 <b>by </b><i>, <a class="ref" href="glib_001.html#T37">GLIB_001:37</a></i>;<br/><b>set </b><font color="Maroon">P</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span>;<br/><a NAME="E7:42_1_2"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">W</font> <a href="glib_001.html#K3">.first()</a> ,<font color="Maroon">W</font> <a href="glib_001.html#K4">.last()</a> 
 <b>by </b><i><a class="ref" href="chord.html#T5" target="_self">Th5</a>, <a class="ref" href="chord.html#T6" target="_self">Th6</a>, <a class="ref" href="glib_001.html#T31">GLIB_001:31</a></i>;<br/><a NAME="E8:42_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="chord.html#T5" target="_self">Th5</a>, <a class="ref" href="chord.html#T6" target="_self">Th6</a>, <a class="ref" href="glib_001.html#T29">GLIB_001:29</a></i>;<br/><a NAME="E9:42_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="chord.html#T7" target="_self">Th7</a>, <a class="ref" href="chord.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:42_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> 1,<font color="Maroon">n</font></span>)</span> <a href="glib_001.html#K7">.append</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E11:42_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="chord.html#T10" target="_self">Th10</a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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