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

<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W1A</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G1</font>, <font color="Maroon">W1B</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">W2A</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G2</font>, <font color="Maroon">W2B</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G2</font>;<br/>







<b>assume </b><a NAME="E1:166"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">W1A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2A</font> &amp; <font color="Maroon">W1B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2B</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="166_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="166_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:166_1_1"/>
( <font color="Maroon">W1A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W1B</font> <a href="glib_001.html#K3" target="_self">.first()</a>  or <font color="Maroon">W1A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W1B</font> <a href="glib_001.html#K3" target="_self">.first()</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="166_1_1_1"><b>suppose </b></a><a NAME="E1:166_1_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">W1A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W1B</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 ;<br/><div class="add"><a NAME="E2:166_1_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">W2A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W2B</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">W1A</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W1B</font> = 
<font color="Maroon">W1A</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">W1B</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">W2A</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2B</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="166_1_1_2"><b>suppose </b></a><a NAME="E1:166_1_1_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">W1A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W1B</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 ;<br/><div class="add"><a NAME="E2:166_1_1_2"/><b>then </b>
<font color="Maroon">W2A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W1B</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 <b>by </b><i/>;<br/><a NAME="E3:166_1_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">W2A</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W2B</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">W1A</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W1B</font> = 
<font color="Maroon">W2A</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">W2A</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2B</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:166"/>
<font color="Maroon">W1A</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W1B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2A</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2B</font>
 ;<br/>


</div>
