<?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">a</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>, <font color="Maroon">b</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:83"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; not <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 ;<br/>

<b>let </b><font color="Maroon">S</font> be    <a href="chord.html#M2" target="_self">VertexSeparator</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>

<a NAME="E2:83"/><i><font color="Green">E33</font></i>: 
( not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:83"/>
for <font color="Olive">G2</font> being  <a href="glib_000.html#NM7">removeVertices</a> of <font color="Maroon">G</font>,<font color="Maroon">S</font><br/> for <font color="Olive">W</font> being   <a href="glib_001.html#M3">Walk</a> of <font color="Olive">G2</font>  holds not <font color="Olive">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM7">removeVertices</a> of <font color="Maroon">G</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G2</font>;<br/>



<b>assume </b><a NAME="E1:83_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:83_1"/>
<font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a>  <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="glib_001.html#T24">GLIB_001:24</a></i>;<br/>
<b>hence </b><a NAME="E3:83_1"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:83"/>
<font color="Maroon">S</font> is    <a href="chord.html#M2" target="_self">VertexSeparator</a> of <font color="Maroon">b</font>,<font color="Maroon">a</font>
 <b>by </b><i>, , </i>;<br/>


</div>
