<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>;<br/>
<b>assume </b><a NAME="E1:181"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> ,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:181"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="txt" href="glib_001.html#E78"><i><font color="Green">Lemma70</font></i></a></i>;<br/>
<a NAME="E3:181"/><b>then </b><i><font color="Green">E130</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <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">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="glib_001.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E4:181"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </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"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E5:181"/><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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E6:181"/><b>then </b>
2 <a href="nat_1.html#K2">*</a> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 
;<br/>
<b>then </b>2 <a href="nat_1.html#K2">*</a> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="ref" href="glib_001.html#D14" target="_self">Def14</a></i>
<br/>.= 
2 <a href="nat_1.html#K2">*</a> <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">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_001.html#E3:181"><i><font color="Green">E130</font></i></a></i>
;<br/>
<a NAME="E8:181"/><b>then </b><i><font color="Green">E131</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="181_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:181_2"/><i><font color="Green">E132</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> )
 ;<br/><a NAME="E2:181_2"/><b>then </b><i><font color="Green">E133</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_001.html#E8:181"><i><font color="Green">E131</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:181_2"/><i><font color="Green">E134</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:181_2"><i><font color="Green">E132</font></i></a>, <a class="ref" href="glib_001.html#D14" target="_self">Def14</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="181_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="181_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:181_2_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="glib_001.html#E2:181_2"><i><font color="Green">E133</font></i></a>, <a class="ref" href="finseq_1.html#T38">FINSEQ_1:38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="181_2_1_1_1"><b>suppose </b></a><a NAME="E1:181_2_1_1_1"/><i><font color="Green">E135</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span>
 ;<br/><div class="add"><a NAME="E2:181_2_1_1_1"/><b>then </b><i><font color="Green">E136</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E3:181_2_1_1_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:181_2_1_1_1"><i><font color="Green">E135</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E4:181_2_1_1_1"/><b>then </b><i><font color="Green">E137</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></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> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="glib_001.html#E2:181_2_1_1_1"><i><font color="Green">E136</font></i></a>, <a class="ref" href="glib_001.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E5:181_2_1_1_1"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:181_2_1_1_1"><i><font color="Green">E135</font></i></a>, <a class="ref" href="glib_001.html#T74" target="_self">Th74</a></i>;<br/><b>hence </b><a NAME="E6:181_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:181"><i><font color="Green">E129</font></i></a>, <a class="txt" href="glib_001.html#E3:181_2"><i><font color="Green">E134</font></i></a>, <a class="txt" href="glib_001.html#E4:181_2_1_1_1"><i><font color="Green">E137</font></i></a>, <a class="txt" href="glib_001.html#E79"><i><font color="Green">Lemma71</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="181_2_1_1_2"><b>suppose </b></a><a NAME="E1:181_2_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:181_2_1_1_2"/><i><font color="Green">E135</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <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">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><a NAME="E4:181_2_1_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E3:181_2_1_1_2"><i><font color="Green">E135</font></i></a>, <a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a></i>;<br/><a NAME="E5:181_2_1_1_2"/><b>then </b><i><font color="Green">E136</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green">E137</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="glib_001.html#E3:181_2_1_1_2"><i><font color="Green">E135</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
;<br/>2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="glib_001.html#E3:181_2_1_1_2"><i><font color="Green">E135</font></i></a>, <a class="txt" href="glib_001.html#E5:181_2_1_1_2"><i><font color="Green">E136</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="ref" href="glib_001.html#D14" target="_self">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/><b>hence </b><a NAME="E8:181_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:181"><i><font color="Green">E129</font></i></a>, <a class="txt" href="glib_001.html#E3:181_2"><i><font color="Green">E134</font></i></a>, <a class="txt" href="glib_001.html#E6:181_2_1_1_2"><i><font color="Green">E137</font></i></a>, <a class="txt" href="glib_001.html#E79"><i><font color="Green">Lemma71</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:181_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:181"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K11" target="_self">.vertexSeq()</a> </span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="glib_001.html#E8:181"><i><font color="Green">E131</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div>
