<?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">W</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">W</font> is <a href="chord.html#V1" target="_self">minlength</a>
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">W</font> is <a href="glib_001.html#V5">Path-like</a>
 ;<br/>

<b>consider </b><font color="Maroon">s</font> being  <a href="glib_001.html#V5">Path-like</a>  <a href="glib_001.html#M4">Subwalk</a> of <font color="Maroon">W</font>;<br/>
<a NAME="E4:41"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">s</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">W</font> <a href="glib_001.html#K3">.first()</a> ,<font color="Maroon">W</font> <a href="glib_001.html#K4">.last()</a> 
 
<b>by </b><i><a class="ref" href="glib_001.html#D32">GLIB_001:def 32</a></i>;<br/>
<a NAME="E5:41"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> )
 
<b>by </b><i><a class="ref" href="glib_001.html#T163">GLIB_001:163</a>, , , </i>;<br/>
<a NAME="E6:41"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T1">XREAL_1:1</a></i>;<br/>
<b>hence </b><a NAME="E7:41"/>
contradiction
 <b>by </b><i>, <a class="txt" href="chord.html#E3"><i><font color="Green">Lemma34</font></i></a></i>;<br/>


</div>
