<?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">S</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="glib_000.html#NM5">inducedSubgraph</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">G</font>;<br/>







<b>assume </b><a NAME="E1:26"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#K13">.vertices()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E2:26"/><i><font color="Green">E33</font></i>: 
(  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> &amp;  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D39">GLIB_000:def 39</a></i>;<br/>
<a NAME="E3:26"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#K13">.vertices()</a>  <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="glib_000.html#D39">GLIB_000:def 39</a></i>;<br/>
<a NAME="E4:26"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#K14">.edges()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="glib_001.html#T110">GLIB_001:110</a></i>;<br/>
<a NAME="E5:26"/>
<font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K13">.vertices()</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="glib_000.html#T39">GLIB_000:39</a></i>;<br/>
<a NAME="E6:26"/><b>then </b>
<font color="Maroon">W</font> <a href="glib_001.html#K14">.edges()</a>  <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">H</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
<font color="Maroon">W</font> is    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="glib_001.html#T171">GLIB_001:171</a></i>;<br/>


</div>
