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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:115_3_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">G</font> is <a href="chord.html#V2" target="_self">complete</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_3_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">W</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font>;<br/><b>assume </b><a NAME="E1:115_3_1_1"/><i><font color="Green">E76</font></i>: 
( <font color="Maroon">W</font> <a href="glib_001.html#K15">.length()</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3 &amp; <font color="Maroon">W</font> is <a href="glib_001.html#V8">Cycle-like</a> )
 ;<br/><a NAME="E2:115_3_1_1"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">W</font> is <a href="glib_001.html#V5">Path-like</a>
 <b>by </b><i>, <a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/><a NAME="E3:115_3_1_1"/>
<font color="Maroon">W</font> <a href="glib_001.html#K15">.length()</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:115_3_1_1"/><b>then </b>
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K15">.length()</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 <a href="nat_1.html#K2">*</a> 4
 <b>by </b><i><a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E5:115_3_1_1"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K15">.length()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E6:115_3_1_1"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 9
 <b>by </b><i><a class="ref" href="glib_001.html#T113">GLIB_001:113</a></i>;<br/><b>reconsider </b><font color="Maroon">t3</font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 as  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a> ;<br/><b>reconsider </b><font color="Maroon">t7</font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1 as  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a> ;<br/><a NAME="E9:115_3_1_1"/>
<font color="Maroon">t3</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>then reconsider </b><font color="Maroon">W3</font> = <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">t3</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> <b>by </b><i><a class="ref" href="glib_001.html#T8">GLIB_001:8</a></i>;<br/><a NAME="E11:115_3_1_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">t7</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>then reconsider </b><font color="Maroon">W7</font> = <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">t7</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> <b>by </b><i><a class="ref" href="glib_001.html#T8">GLIB_001:8</a></i>;<br/><a NAME="E13:115_3_1_1"/>
<font color="Maroon">W3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W7</font>
 <b>by </b><i>, , <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><a NAME="E14:115_3_1_1"/><b>then </b>
<font color="Maroon">W3</font>,<font color="Maroon">W7</font> <a href="chord.html#R1" target="_self">are_adjacent</a> 
 <b>by </b><i><a class="ref" href="chord.html#T19" target="_self">Th19</a>, </i>;<br/><b>then consider </b><font color="Maroon">e</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E16:115_3_1_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W3</font>,<font color="Maroon">W7</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="chord.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E17:115_3_1_1"/>
( <font color="Maroon">t3</font> <a href="xcmplx_0.html#K2">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">t7</font> &amp; <font color="Maroon">t7</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> &amp; (  not <font color="Maroon">t3</font> <a href="hidden.html#R1">=</a> 3 or  not <font color="Maroon">t7</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> ) )
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E18:115_3_1_1"/>
<font color="Maroon">W</font> is <a href="chord.html#V5" target="_self">chordal</a>
 <b>by </b><i>, , <a class="txt" href="chord.html#E11:115_3_1_1"><i><font color="Green">E82</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:115_3_1"/>
<font color="Maroon">G</font> is <a href="chord.html#V6" target="_self">chordal</a>
 <b>by </b><i/>;<br/>


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