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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G2</font> being   <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Olive" title="b2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Olive" title="b2">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>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Olive" title="b1">G2</font> holds <br/><font color="Olive" title="b2">W</font> is    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Olive" title="b1">G2</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Olive" title="b1">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Olive" title="b1">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>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font> holds <br/><font color="Olive" title="b1">W</font> is    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <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>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font> implies <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> )</span><br/>





<b>assume </b><a NAME="E1:239"/><i><font color="Green" title="E149">A1</font></i>: 
( <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <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>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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></span><br/>

<b>then consider </b><font color="Maroon" title="c4">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><b> such that </b><br/><a NAME="E3:239"/><i><font color="Green" title="E150">A2</font></i>: 
<font color="Maroon" title="c3">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c4">v</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E93"><i><font color="Green" title="E85">Lm56</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">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="c2">G2</font> <b>by </b><i><a class="txt" href="glib_001.html#E1:239"><i><font color="Green" title="E149">A1</font></i></a>, <a class="txt" href="glib_001.html#E3:239"><i><font color="Green" title="E150">A2</font></i></a>, <a class="ref" href="glib_001.html#T14" target="_self" title="GLIB_001:th.14">Th14</a></i>;<br/>
<a NAME="E5:239"/>
<font color="Maroon" title="c3">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c5">v'</font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E3:239"><i><font color="Green" title="E150">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:239"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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