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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>;<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>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c2">W</font> is <a href="chord.html#V1" title="CHORD:attr.1">minlength</a>
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green" title="E36">A2</font></i>: 
not <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">s</font> being  <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>  <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c2">W</font>;<br/>
<a NAME="E4:41"/>
<font color="Maroon" title="c3">s</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 
<b>by </b><i><a class="ref" href="glib_001.html#D32" title="GLIB_001:def.32">GLIB_001:def 32</a></i>;<br/>
<a NAME="E5:41"/><b>then </b>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s</font> )
 
<b>by </b><i><a class="txt" href="chord.html#E1:41"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="chord.html#D2" target="_self" title="CHORD:def.2">Def2</a>, <a class="ref" href="glib_001.html#T163" title="GLIB_001:th.163">GLIB_001:163</a></i>;<br/>
<b>hence </b><a NAME="E6:41"/>
contradiction
 <b>by </b><i><a class="txt" href="chord.html#E2:41"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="chord.html#T35" target="_self" title="CHORD:th.35">Th35</a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>


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