<?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>assume </b><a NAME="E1:65"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">G1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">G1</font> is <a href="glib_002.html#V1" target="_self">connected</a> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>, <font color="Maroon">v</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>;<br/><b>reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font>, <font color="Maroon">v'</font> = <font color="Maroon">v</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G1</font> <b>by </b><i>, <a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>;<br/><b>consider </b><font color="Maroon">W'</font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G1</font><b> such that </b><br/><a NAME="E3:65_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">W'</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">u'</font>,<font color="Maroon">v'</font>
 <b>by </b><i>, </i>;<br/><b>reconsider </b><font color="Maroon">W</font> = <font color="Maroon">W'</font> as    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G2</font> <b>by </b><i>, <a class="ref" href="glib_001.html#T180">GLIB_001:180</a></i>;<br/><b>take </b><font color="Maroon">W</font> = <font color="Maroon">W</font>;<br/><b>thus </b><a NAME="E5:65_1"/>
<font color="Maroon">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">u</font>,<font color="Maroon">v</font>
 <b>by </b><i>, <a class="ref" href="glib_001.html#T20">GLIB_001:20</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:65"/>
<font color="Maroon">G2</font> is <a href="glib_002.html#V1" target="_self">connected</a>
 <b>by </b><i/>;<br/>


</div>
