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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><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">G1</font>;<br/><b>let </b><font color="Maroon" title="c4">W2</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font>;<br/>







<b>set </b><font color="Maroon" title="c5">VS1</font> = <font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">VS2</font> = <font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> ;<br/>
<b>assume </b><a NAME="E1:182"/><i><font color="Green" title="E125">A1</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="182_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:182_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span>
 ;<br/><i><font color="Green" title="E126">A2</font></i>: 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">W2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<b>by </b><i><a class="txt" href="glib_001.html#E1:182"><i><font color="Green" title="E125">A1</font></i></a>, <a class="ref" href="glib_001.html#D14" target="_self" title="GLIB_001:def.14">Def14</a></i>
<br/>.= 
2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="glib_001.html#D14" target="_self" title="GLIB_001:def.14">Def14</a></i>
;<br/><b>hence </b><a NAME="E3:182_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span>
 ;<br/><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E4:182_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E5:182_1"/><b>then </b>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E6:182_1"/><b>then </b><i><font color="Green" title="E127">A3</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">x</font> &amp; <font color="Maroon" title="c7">x</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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span> &amp; <font color="Maroon" title="c7">x</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E2:182_1"><i><font color="Green" title="E126">A2</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<font color="Maroon" title="c4">W2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c7">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="glib_001.html#E1:182"><i><font color="Green" title="E125">A1</font></i></a>, <a class="ref" href="glib_001.html#D14" target="_self" title="GLIB_001:def.14">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="glib_001.html#E6:182_1"><i><font color="Green" title="E127">A3</font></i></a>, <a class="ref" href="glib_001.html#D14" target="_self" title="GLIB_001:def.14">Def14</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:182"/>
<font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a> 
 <b>by </b><i><a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


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