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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">W2</font>, <font color="Maroon" title="c3">W1</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>assume </b><a NAME="E1:219"/><i><font color="Green" title="E150">A1</font></i>: 
( not <font color="Maroon" title="c2">W2</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c2">W2</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  )
 ;<br/>

<a NAME="E2:219"/><b>then </b><i><font color="Green" title="E151">A2</font></i>: 
3 <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="c2">W2</font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E96"><i><font color="Green" title="E88">Lm59</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="219_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:219_1"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 ;<br/><b>then consider </b><font color="Maroon" title="c5">n</font> being  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:219_1"/><i><font color="Green" title="E152">A3</font></i>: 
( <font color="Maroon" title="c5">n</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> <font color="Maroon" title="c2">W2</font> &amp; <font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E86"><i><font color="Green" title="E78">Lm49</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="219_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="219_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:219_1_1_1"/>
( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W2</font> or <font color="Maroon" title="c5">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="219_1_1_1_1"><b>suppose </b></a><a NAME="E1:219_1_1_1_1"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W2</font>
 ;<br/><div class="add"><a NAME="E2:219_1_1_1_1"/><b>then </b>
3 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0
 <b>by </b><i><a class="txt" href="glib_001.html#E2:219"><i><font color="Green" title="E151">A2</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c6">n5</font> = <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a></i>;<br/><a NAME="E4:219_1_1_1_1"/>
<font color="Maroon" title="c6">n5</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E5:219_1_1_1_1"/><b>then </b><i><font color="Green" title="E153">A4</font></i>: 
<font color="Maroon" title="c6">n5</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> <font color="Maroon" title="c2">W2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E3:219_1"><i><font color="Green" title="E152">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:219_1_1_1_1"/><b>then </b><i><font color="Green" title="E154">A5</font></i>: 
<font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n5</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n5</font>,<font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n5</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D3" target="_self" title="GLIB_001:def.3">Def3</a></i>;<br/><a NAME="E7:219_1_1_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n5</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c6">n5</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c2">W2</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E5:219_1_1_1_1"><i><font color="Green" title="E153">A4</font></i></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:219_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n5</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E87"><i><font color="Green" title="E79">Lm50</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">m</font> being  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E10:219_1_1_1_1"/><i><font color="Green" title="E155">A6</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">m</font> &amp; <font color="Maroon" title="c7">m</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> <font color="Maroon" title="c3">W1</font> &amp; <font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n5</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:219"><i><font color="Green" title="E150">A1</font></i></a>, <a class="txt" href="glib_001.html#E87"><i><font color="Green" title="E79">Lm50</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">maa1</font> = <font color="Maroon" title="c7">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="glib_001.html#E10:219_1_1_1_1"><i><font color="Green" title="E155">A6</font></i></a>, <a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a></i>;<br/><a NAME="E12:219_1_1_1_1"/><i><font color="Green" title="E156">A7</font></i>: 
<font color="Maroon" title="c8">maa1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">W1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0
 <b>by </b><i><a class="txt" href="glib_001.html#E10:219_1_1_1_1"><i><font color="Green" title="E155">A6</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E13:219_1_1_1_1"/><b>then </b><i><font color="Green" title="E157">A8</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">maa1</font>,<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D3" target="_self" title="GLIB_001:def.3">Def3</a></i>;<br/><a NAME="E14:219_1_1_1_1"/><i><font color="Green" title="E158">A9</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">maa1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <font color="Maroon" title="c8">maa1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E12:219_1_1_1_1"><i><font color="Green" title="E156">A7</font></i></a>, <a class="ref" href="glib_001.html#D8" target="_self" title="GLIB_001:def.8">Def8</a></i>;<br/><a NAME="E15:219_1_1_1_1"/><i><font color="Green" title="E159">A10</font></i>: 
<font color="Maroon" title="c8">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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> <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E12:219_1_1_1_1"><i><font color="Green" title="E156">A7</font></i></a>, <a class="ref" href="glib_001.html#T1" target="_self" title="GLIB_001:th.1">Th1</a></i>;<br/><a NAME="E16:219_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="glib_001.html#D8" target="_self" title="GLIB_001:def.8">Def8</a></i>;<br/><a NAME="E17:219_1_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <font color="Maroon" title="c8">maa1</font> or <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> )
 <b>by </b><i><a class="ref" href="glib_000.html#T18" title="GLIB_000:th.18">GLIB_000:18</a>, <a class="txt" href="glib_001.html#E10:219_1_1_1_1"><i><font color="Green" title="E155">A6</font></i></a>, <a class="txt" href="glib_001.html#E3:219_1"><i><font color="Green" title="E152">A3</font></i></a>, <a class="txt" href="glib_001.html#E6:219_1_1_1_1"><i><font color="Green" title="E154">A5</font></i></a>, <a class="txt" href="glib_001.html#E13:219_1_1_1_1"><i><font color="Green" title="E157">A8</font></i></a>, <a class="txt" href="glib_001.html#E14:219_1_1_1_1"><i><font color="Green" title="E158">A9</font></i></a></i>;<br/><b>hence </b><a NAME="E18:219_1_1_1_1"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E12:219_1_1_1_1"><i><font color="Green" title="E156">A7</font></i></a>, <a class="txt" href="glib_001.html#E15:219_1_1_1_1"><i><font color="Green" title="E159">A10</font></i></a>, <a class="ref" href="glib_001.html#T90" target="_self" title="GLIB_001:th.90">Th90</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="219_1_1_1_2"><b>suppose </b></a><a NAME="E1:219_1_1_1_2"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W2</font>
 ;<br/><div class="add"><a NAME="E2:219_1_1_1_2"/><b>then </b><i><font color="Green" title="E153">A11</font></i>: 
<font color="Maroon" title="c5">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> <font color="Maroon" title="c2">W2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E3:219_1"><i><font color="Green" title="E152">A3</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:219_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#T101" target="_self" title="GLIB_001:th.101">Th101</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">m</font> being  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E5:219_1_1_1_2"/><i><font color="Green" title="E154">A12</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m</font> &amp; <font color="Maroon" title="c6">m</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> <font color="Maroon" title="c3">W1</font> &amp; <font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:219"><i><font color="Green" title="E150">A1</font></i></a>, <a class="txt" href="glib_001.html#E87"><i><font color="Green" title="E79">Lm50</font></i></a></i>;<br/><a NAME="E6:219_1_1_1_2"/><i><font color="Green" title="E155">A13</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c2">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E2:219_1_1_1_2"><i><font color="Green" title="E153">A11</font></i></a>, <a class="txt" href="glib_001.html#E3:219_1"><i><font color="Green" title="E152">A3</font></i></a>, <a class="txt" href="glib_001.html#E5:219_1_1_1_2"><i><font color="Green" title="E154">A12</font></i></a>, <a class="ref" href="glib_001.html#D3" target="_self" title="GLIB_001:def.3">Def3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">maa1</font> = <font color="Maroon" title="c6">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="glib_001.html#E5:219_1_1_1_2"><i><font color="Green" title="E154">A12</font></i></a>, <a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a></i>;<br/><a NAME="E8:219_1_1_1_2"/><i><font color="Green" title="E156">A14</font></i>: 
<font color="Maroon" title="c7">maa1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">W1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0
 <b>by </b><i><a class="txt" href="glib_001.html#E5:219_1_1_1_2"><i><font color="Green" title="E154">A12</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E9:219_1_1_1_2"/><b>then </b><i><font color="Green" title="E157">A15</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">maa1</font>,<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D3" target="_self" title="GLIB_001:def.3">Def3</a></i>;<br/><a NAME="E10:219_1_1_1_2"/><i><font color="Green" title="E158">A16</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">maa1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <font color="Maroon" title="c7">maa1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E8:219_1_1_1_2"><i><font color="Green" title="E156">A14</font></i></a>, <a class="ref" href="glib_001.html#D8" target="_self" title="GLIB_001:def.8">Def8</a></i>;<br/><a NAME="E11:219_1_1_1_2"/><i><font color="Green" title="E159">A17</font></i>: 
<font color="Maroon" title="c7">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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> <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E8:219_1_1_1_2"><i><font color="Green" title="E156">A14</font></i></a>, <a class="ref" href="glib_001.html#T1" target="_self" title="GLIB_001:th.1">Th1</a></i>;<br/><a NAME="E12:219_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">W1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="glib_001.html#D8" target="_self" title="GLIB_001:def.8">Def8</a></i>;<br/><a NAME="E13:219_1_1_1_2"/><b>then </b>
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <font color="Maroon" title="c7">maa1</font> or <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">maa1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> )
 <b>by </b><i><a class="ref" href="glib_000.html#T18" title="GLIB_000:th.18">GLIB_000:18</a>, <a class="txt" href="glib_001.html#E9:219_1_1_1_2"><i><font color="Green" title="E157">A15</font></i></a>, <a class="txt" href="glib_001.html#E10:219_1_1_1_2"><i><font color="Green" title="E158">A16</font></i></a>, <a class="txt" href="glib_001.html#E6:219_1_1_1_2"><i><font color="Green" title="E155">A13</font></i></a></i>;<br/><b>hence </b><a NAME="E14:219_1_1_1_2"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E8:219_1_1_1_2"><i><font color="Green" title="E156">A14</font></i></a>, <a class="txt" href="glib_001.html#E11:219_1_1_1_2"><i><font color="Green" title="E159">A17</font></i></a>, <a class="ref" href="glib_001.html#T90" target="_self" title="GLIB_001:th.90">Th90</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:219_1"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:219"/>
<font color="Maroon" title="c2">W2</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


</div>
