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

<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W1</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/>





<b>set </b><font color="Maroon">W</font> = <font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font>;<br/>
<b>set </b><font color="Maroon">WV</font> = <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K13" target="_self">.vertices()</a> ;<br/>
<b>set </b><font color="Maroon">W1V</font> = <font color="Maroon">W1</font> <a href="glib_001.html#K13" target="_self">.vertices()</a> ;<br/>
<b>set </b><font color="Maroon">W2V</font> = <font color="Maroon">W2</font> <a href="glib_001.html#K13" target="_self">.vertices()</a> ;<br/>
<b>set </b><font color="Maroon">WE</font> = <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a> ;<br/>
<b>set </b><font color="Maroon">W1E</font> = <font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> ;<br/>
<b>set </b><font color="Maroon">W2E</font> = <font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> ;<br/>
<b>assume </b><a NAME="E1:200"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">W1</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 ;<br/>

<a NAME="E2:200"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">W2</font>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">lenW1</font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font>;<br/>
<b>set </b><font color="Maroon">lenW2</font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font>;<br/>
<b>reconsider </b><font color="Maroon">lenW1</font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font>, <font color="Maroon">lenW2</font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font> as  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="200_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:200_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 ;<br/><b>then consider </b><font color="Maroon">n</font> being  <a href="abian.html#V1">even</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:200_1_1"/><i><font color="Green">E42</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</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">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="200_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:200_1_1_1_1"/>
( <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:200_1_1_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font>
 ;<br/><div class="add"><a NAME="E2:200_1_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E40"><i><font color="Green">Lemma142</font></i></a>, <a class="txt" href="glib_001.html#E41"><i><font color="Green">Lemma143</font></i></a>, <a class="ref" href="graph_2.html#T14">GRAPH_2:14</a></i>;<br/><a NAME="E3:200_1_1_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E41"><i><font color="Green">Lemma143</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E4:200_1_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:200_1_1_1_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">k</font> = <font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">lenW1</font> as  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/><a NAME="E3:200_1_1_1_1_2"/><i><font color="Green">E44</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><a NAME="E4:200_1_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">lenW1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E41"><i><font color="Green">Lemma143</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:200_1_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">lenW1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">lenW1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">lenW2</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_001.html#D31" target="_self">Def31</a>, <a class="txt" href="glib_001.html#E3:200_1_1"><i><font color="Green">E42</font></i></a></i>;<br/><a NAME="E6:200_1_1_1_1_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">lenW2</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span>
 <b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><b>then </b><i><font color="Green">E46</font></i>: <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="txt" href="glib_001.html#E40"><i><font color="Green">Lemma142</font></i></a>, , <a class="ref" href="graph_2.html#T15">GRAPH_2:15</a></i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="glib_001.html#E41"><i><font color="Green">Lemma143</font></i></a></i>
;<br/><a NAME="E8:200_1_1_1_1_2"/><i><font color="Green">E47</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E9:200_1_1_1_1_2"/>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E42"><i><font color="Green">Lemma145</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E10:200_1_1_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E43"><i><font color="Green">Lemma146</font></i></a>, <a class="txt" href="glib_001.html#E44"><i><font color="Green">Lemma147</font></i></a>, </i>;<br/><b>hence </b><a NAME="E11:200_1_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:200_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span>
 ;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:200_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="200_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:200_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a>  )
 </span><b>by </b><i><a class="txt" href="glib_001.html#E41"><i><font color="Green">Lemma143</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2_1_1"><b>suppose </b></a><a NAME="E1:200_1_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">n</font> being  <a href="abian.html#V1">even</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:200_1_2_1_1"/><i><font color="Green">E49</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</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">W1</font> &amp; <font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/><a NAME="E4:200_1_2_1_1"/><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E40"><i><font color="Green">Lemma142</font></i></a>, , <a class="ref" href="graph_2.html#T14">GRAPH_2:14</a></i>;<br/><a NAME="E5:200_1_2_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</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">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_001.html#D31" target="_self">Def31</a>, </i>;<br/><a NAME="E6:200_1_2_1_1"/><b>then </b>
<font color="Maroon">n</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">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E7:200_1_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 <b>by </b><i>, <a class="txt" href="glib_001.html#E42"><i><font color="Green">Lemma145</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2_1_2"><b>suppose </b></a><a NAME="E1:200_1_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">n</font> being  <a href="abian.html#V1">even</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:200_1_2_1_2"/><i><font color="Green">E52</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</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">W2</font> &amp; <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">naa1</font> = <font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> 1 as  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/><a NAME="E5:200_1_2_1_2"/><i><font color="Green">E53</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">naa1</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><a NAME="E6:200_1_2_1_2"/>
<font color="Maroon">naa1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font>
 <b>by </b><i>, <a class="ref" href="sppol_1.html#T5">SPPOL_1:5</a></i>;<br/><b>then </b><i><font color="Green">E56</font></i>: <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">lenW1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">naa1</font></span>)</span> = 
<font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">naa1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="glib_001.html#E40"><i><font color="Green">Lemma142</font></i></a>, <a class="txt" href="glib_001.html#E42"><i><font color="Green">Lemma145</font></i></a>, <a class="ref" href="graph_2.html#T15">GRAPH_2:15</a></i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i/>
;<br/><a NAME="E8:200_1_2_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">lenW1</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><a NAME="E9:200_1_2_1_2"/><b>then </b><i><font color="Green">E88</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">lenW1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">naa1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E10:200_1_2_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">naa1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">lenW1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E11:200_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">lenW1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">naa1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="glib_001.html#D31" target="_self">Def31</a>, </i>;<br/><a NAME="E12:200_1_2_1_2"/><b>then </b>
<font color="Maroon">lenW1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">naa1</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">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E13:200_1_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E43"><i><font color="Green">Lemma146</font></i></a>, <a class="txt" href="glib_001.html#E44"><i><font color="Green">Lemma147</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="E4:200_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:200"/>
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
