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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>



<b>assume </b><a NAME="E1:65"/><i><font color="Green" title="E44">A1</font></i>: 
( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">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" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>;<br/><b>reconsider </b><font color="Maroon" title="c5">u'</font> = <font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c6">v'</font> = <font color="Maroon" title="c4">v</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="txt" href="glib_002.html#E1:65"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">W'</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font><b> such that </b><br/><a NAME="E3:65_1"/><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c7">W'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c6">v'</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:65"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">W</font> = <font color="Maroon" title="c7">W'</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font> <b>by </b><i><a class="txt" href="glib_002.html#E1:65"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="glib_001.html#T180" title="GLIB_001:th.180">GLIB_001:180</a></i>;<br/><b>take </b><font color="Maroon" title="c9">W</font> = <font color="Maroon" title="c8">W</font>;<br/><b>thus </b><a NAME="E5:65_1"/>
<font color="Maroon" title="c9">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:65_1"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:65"/>
<font color="Maroon" title="c2">G2</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/>


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