<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>  st <font color="Olive" title="b1">W</font> is  <a href="chord.html#V1" title="CHORD:attr.1">minlength</a>  holds <br/><font color="Olive" title="b1">W</font> is  <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> </span><br/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">W</font> is  <a href="chord.html#V1" title="CHORD:attr.1">minlength</a>  implies <font color="Maroon" title="c2">W</font> is  <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:39"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c2">W</font> is  <a href="chord.html#V1" title="CHORD:attr.1">minlength</a> 
 <span class="kw">and </span><br/><a NAME="E2:39"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
 not <font color="Maroon" title="c2">W</font> is  <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">s</font> =  the   <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="E3:39"/>
 the   <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> <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D32" onmouseover="rs('glib_001/D32')" onmouseout="rh()">GLIB_001:def 32</a></span>;<br/>
<a NAME="E4:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A3</font></span>: 
 <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>  the   <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E36">A1</font></span></a></span>;<br/>
<a NAME="E5:39"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a>  the   <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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T162" onmouseover="rs('glib_001/T162')" onmouseout="rh()">GLIB_001:162</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:39"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="chord.html#T35" target="_self" onmouseover="rs('chord/T35')" onmouseout="rh()">Th35</a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
