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

<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>, <font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:27"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">G1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">G2</font>
 ;<br/>

<b>let </b><font color="Maroon">W1</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G2</font>;<br/>



<b>assume </b><a NAME="E2:27"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font>
 ;<br/>

<b>assume </b><a NAME="E3:27"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">W1</font> is <a href="glib_001.html#V8">Cycle-like</a>
 ;<br/>

<a NAME="E4:27"/>
<font color="Maroon">W1</font> is <a href="glib_001.html#V5">Path-like</a>
 
<b>by </b><i>, <a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E5:27"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">W2</font> is <a href="glib_001.html#V5">Path-like</a>
 
<b>by </b><i>, , <a class="ref" href="glib_001.html#T182">GLIB_001:182</a></i>;<br/>
<a NAME="E6:27"/>
not <font color="Maroon">W1</font> is <a href="glib_001.html#V3">trivial</a>
 
<b>by </b><i>, <a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E7:27"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="glib_001.html#T127">GLIB_001:127</a></i>;<br/>
<a NAME="E8:27"/><b>then </b><i><font color="Green">E59</font></i>: 
not <font color="Maroon">W2</font> is <a href="glib_001.html#V3">trivial</a>
 
<b>by </b><i><a class="ref" href="glib_001.html#T127">GLIB_001:127</a></i>;<br/>
<a NAME="E9:27"/>
<font color="Maroon">W1</font> is <a href="glib_001.html#V1">closed</a>
 
<b>by </b><i>, <a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E10:27"/><b>then </b>
<font color="Maroon">W1</font> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> <a href="glib_001.html#K4">.last()</a> 
 
<b>by </b><i><a class="ref" href="glib_001.html#D24">GLIB_001:def 24</a></i>;<br/>
<a NAME="E11:27"/><b>then </b>
<font color="Maroon">W2</font> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K4">.last()</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E12:27"/><b>then </b>
<font color="Maroon">W2</font> is <a href="glib_001.html#V1">closed</a>
 
<b>by </b><i><a class="ref" href="glib_001.html#D24">GLIB_001:def 24</a></i>;<br/>
<b>hence </b><a NAME="E13:27"/>
<font color="Maroon">W2</font> is <a href="glib_001.html#V8">Cycle-like</a>
 <b>by </b><i><a class="ref" href="chord.html#T1" target="_self">Th1</a>, , <a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/>


</div>
