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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:113"/><i><font color="Green" title="E90">A1</font></i>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font>
 ;<br/>

<b>assume </b><a NAME="E2:113"/><i><font color="Green" title="E91">A2</font></i>: 
<font color="Maroon" title="c1">G1</font> is <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_1"><b>now </b></a><div class="add"><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="c2">G2</font>;<br/><b>assume </b><a NAME="E1:113_1"/><i><font color="Green" title="E92">A3</font></i>: 
( <font color="Maroon" title="c3">W</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 &amp; <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> )
 ;<br/><b>reconsider </b><font color="Maroon" title="c4">W2</font> = <font color="Maroon" title="c3">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="txt" href="chord.html#E1:113"><i><font color="Green" title="E90">A1</font></i></a>, <a class="ref" href="glib_001.html#T180" title="GLIB_001:th.180">GLIB_001:180</a></i>;<br/><a NAME="E3:113_1"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">W</font>
 <b>by </b><i><a class="ref" href="glib_001.html#T113" title="GLIB_001:th.113">GLIB_001:113</a></i>;<br/><a NAME="E4:113_1"/><b>then </b><i><font color="Green" title="E93">A4</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">W</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="glib_001.html#T113" title="GLIB_001:th.113">GLIB_001:113</a></i>;<br/><a NAME="E5:113_1"/>
<font color="Maroon" title="c4">W2</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>
 <b>by </b><i><a class="txt" href="chord.html#E1:113_1"><i><font color="Green" title="E92">A3</font></i></a>, <a class="txt" href="chord.html#E1:113"><i><font color="Green" title="E90">A1</font></i></a>, <a class="ref" href="chord.html#T24" target="_self" title="CHORD:th.24">Th24</a></i>;<br/><a NAME="E6:113_1"/><b>then </b>
<font color="Maroon" title="c4">W2</font> is <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>
 <b>by </b><i><a class="txt" href="chord.html#E4:113_1"><i><font color="Green" title="E93">A4</font></i></a>, <a class="txt" href="chord.html#E1:113_1"><i><font color="Green" title="E92">A3</font></i></a>, <a class="txt" href="chord.html#E2:113"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="chord.html#D11" target="_self" title="CHORD:def.11">Def11</a></i>;<br/><b>hence </b><a NAME="E7:113_1"/>
<font color="Maroon" title="c3">W</font> is <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>
 <b>by </b><i><a class="txt" href="chord.html#E1:113"><i><font color="Green" title="E90">A1</font></i></a>, <a class="ref" href="chord.html#T86" target="_self" title="CHORD:th.86">Th86</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:113"/>
<font color="Maroon" title="c2">G2</font> is <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>
 <b>by </b><i><a class="ref" href="chord.html#D11" target="_self" title="CHORD:def.11">Def11</a></i>;<br/>


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