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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <font color="Maroon" title="c1">G1</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c2">G2</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:112"/><span class="lab"><font color="Green" title="E89">A1</font></span>: 
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">G1</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  or <font color="Maroon" title="c2">G2</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:112"/><span class="lab"><font color="Green" title="E90">A2</font></span>: 
<font color="Maroon" title="c1">G1</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="112_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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>  implies <font color="Maroon" title="c3">W</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>  )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:112_1"/><span class="lab"><font color="Green" title="E91">A3</font></span>: 
<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
 <span class="kw">and </span><br/><a NAME="E2:112_1"/><span class="lab"><font color="Green" title="E92">A4</font></span>: 
<font color="Maroon" title="c3">W</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">W</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a> </span><br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E89">A1</font></span></a>, <a class="ref" href="glib_001.html#T179" title="GLIB_001:th.179">GLIB_001:179</a></span>;<br/><a NAME="E4:112_1"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</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#K2" title="NAT_1:func.2">+</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T112" title="GLIB_001:th.112">GLIB_001:112</a></span>;<br/><a NAME="E5:112_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A5</font></span>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</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#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</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#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T112" title="GLIB_001:th.112">GLIB_001:112</a></span>;<br/><a NAME="E6:112_1"/>
<font color="Maroon" title="c4">W2</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E89">A1</font></span></a>, <a class="txt" href="#E2:112_1"><span class="lab"><font color="Green" title="E92">A4</font></span></a>, <a class="ref" href="chord.html#T24" target="_self" title="CHORD:th.24">Th24</a></span>;<br/><a NAME="E7:112_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">W2</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E90">A2</font></span></a>, <a class="txt" href="#E1:112_1"><span class="lab"><font color="Green" title="E91">A3</font></span></a>, <a class="txt" href="#E5:112_1"><span class="lab"><font color="Green" title="E93">A5</font></span></a>, <a class="ref" href="chord.html#D11" target="_self" title="CHORD:def.11">Def11</a></span>;<br/><span class="kw">hence </span><a NAME="E8:112_1"/>
<font color="Maroon" title="c3">W</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E89">A1</font></span></a>, <a class="ref" href="chord.html#T86" target="_self" title="CHORD:th.86">Th86</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:112"/>
<font color="Maroon" title="c2">G2</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D11" target="_self" title="CHORD:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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