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<b>let </b><font color="Maroon" title="c1">G</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">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Olive" title="b1">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> iff  ex <font color="Olive" title="b2">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b2">v</font> )</span><br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> iff  ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c2">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> )</span><br/>



<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c2">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> implies <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:90_1"/>
<font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c2">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font></span><br/><a NAME="E2:90_1"/><b>then </b><i><font color="Green" title="E86">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E92"><i><font color="Green" title="E84">Lm55</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c3">v</font> = <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c3">v</font></span><br/><b>thus </b><a NAME="E3:90_1"/>
<font color="Maroon" title="c2">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c3">v</font>
 <b>by </b><i><a class="txt" href="#E2:90_1"><i><font color="Green" title="E86">A1</font></i></a>, <a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c3">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><b> such that </b><a NAME="E3:90"/><i><font color="Green" title="E86">A2</font></i>: 
<font color="Maroon" title="c2">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c3">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a></span><br/>

<a NAME="E4:90"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="#E3:90"><i><font color="Green" title="E86">A2</font></i></a>, <a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<b>hence </b><a NAME="E5:90"/>
<font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 <b>by </b><i><a class="txt" href="glib_001.html#E92"><i><font color="Green" title="E84">Lm55</font></i></a></i>; <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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