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<b>let </b><font color="Maroon" title="c1">G1</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">G2</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c3">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font>;<br/>





<b>assume </b><a NAME="E1:241"/><i><font color="Green" title="E158">A1</font></i>: 
( <font color="Maroon" title="c3">W</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c3">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G2</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="241_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="241_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:241_1_1"/>
(  not <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> or <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="241_1_1_1"><b>suppose </b></a><a NAME="E1:241_1_1_1"/>
not <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:241_1_1_1"/>
<font color="Maroon" title="c3">W</font> is    <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_001.html#E1:241"><i><font color="Green" title="E158">A1</font></i></a>, <a class="ref" href="glib_001.html#T170" target="_self" title="GLIB_001:th.170">Th170</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="241_1_1_2"><b>suppose </b></a><a NAME="E1:241_1_1_2"/><i><font color="Green" title="E159">A2</font></i>: 
<font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 ;<br/><div class="add"><a NAME="E2:241_1_1_2"/>
<font color="Maroon" title="c3">W</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#T89" target="_self" title="GLIB_001:th.89">Th89</a></i>;<br/><b>hence </b><a NAME="E3:241_1_1_2"/>
<font color="Maroon" title="c3">W</font> is    <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_001.html#E1:241"><i><font color="Green" title="E158">A1</font></i></a>, <a class="txt" href="glib_001.html#E1:241_1_1_2"><i><font color="Green" title="E159">A2</font></i></a>, <a class="ref" href="glib_001.html#T169" target="_self" title="GLIB_001:th.169">Th169</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:241"/>
<font color="Maroon" title="c3">W</font> is    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font>
 ;<br/>


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