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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">S</font> being   <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">S</font> is <a href="chord.html#V7" title="CHORD:attr.7">perfect</a> implies <font color="Maroon" title="c1">G</font> is <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> )</span><br/>

<b>given </b><font color="Maroon" title="c2">S</font> being    <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c1">G</font><b> such that </b><a NAME="E2:137"/><i><font color="Green" title="E99">A1</font></i>: 
<font color="Maroon" title="c2">S</font> is <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G</font> is <a href="chord.html#V6" title="CHORD:attr.6">chordal</a></span><br/>

<b>let </b><font color="Maroon" title="c3">P</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="chord.html#D11" target="_self" title="CHORD:def.11">CHORD:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">P</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">P</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> implies <font color="Maroon" title="c3">P</font> is <a href="chord.html#V5" title="CHORD:attr.5">chordal</a> )</span><br/>

<b>assume </b><a NAME="E3:137"/><i><font color="Green" title="E100">A2</font></i>: 
( <font color="Maroon" title="c3">P</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">P</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">P</font> is <a href="chord.html#V5" title="CHORD:attr.5">chordal</a></span><br/>

<a NAME="E4:137"/><i><font color="Green" title="E101">A3</font></i>: 
<font color="Maroon" title="c3">P</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 
<b>by </b><i><a class="txt" href="chord.html#E3:137"><i><font color="Green" title="E100">A2</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E5:137"/><i><font color="Green" title="E102">A4</font></i>: 
not <font color="Maroon" title="c3">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="ref" href="glib_001.html#T89" title="GLIB_001:th.89">GLIB_001:89</a></i>;<br/>
<a NAME="E6:137"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:137"/><i><font color="Green" title="E103">A5</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>and </b><br/><a NAME="E9:137"/><i><font color="Green" title="E104">A6</font></i>: 
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  holds <br/><font color="Maroon" title="c4">x</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">y</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="chord.html#E5:137"><i><font color="Green" title="E102">A4</font></i></a>, <a class="ref" href="chord.html#T15" target="_self" title="CHORD:th.15">Th15</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c4">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="chord.html#E8:137"><i><font color="Green" title="E103">A5</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">n</font> = <font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font>;<br/>
<a NAME="E11:137"/><i><font color="Green" title="E105">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></i>;<br/>
<a NAME="E12:137"/><b>then </b><i><font color="Green" title="E106">A8</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">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">S</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T31" title="FINSEQ_4:th.31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E13:137"/><i><font color="Green" title="E107">A9</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="chord.html#E11:137"><i><font color="Green" title="E105">A7</font></i></a>, <a class="ref" href="finseq_4.html#T30" title="FINSEQ_4:th.30">FINSEQ_4:30</a></i>;<br/>
<a NAME="E14:137"/><i><font color="Green" title="E108">A10</font></i>: 
<font color="Maroon" title="c2">S</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  implies <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span> )</span><br/><b>assume </b><a NAME="E1:137_1"/><i><font color="Green" title="E109">A11</font></i>: 
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span></span><br/><b>reconsider </b><font color="Maroon" title="c8">z</font> = <font color="Maroon" title="c7">y</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="chord.html#E1:137_1"><i><font color="Green" title="E109">A11</font></i></a></i>;<br/><a NAME="E3:137_1"/>
<font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">z</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="chord.html#E9:137"><i><font color="Green" title="E104">A6</font></i></a>, <a class="txt" href="chord.html#E1:137_1"><i><font color="Green" title="E109">A11</font></i></a></i>;<br/><b>hence </b><a NAME="E4:137_1"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span>
 <b>by </b><i><a class="txt" href="chord.html#E11:137"><i><font color="Green" title="E105">A7</font></i></a>, <a class="txt" href="chord.html#E13:137"><i><font color="Green" title="E107">A9</font></i></a>, <a class="txt" href="chord.html#E14:137"><i><font color="Green" title="E108">A10</font></i></a>, <a class="ref" href="chord.html#T16" target="_self" title="CHORD:th.16">Th16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E16:137"/><b>then </b><i><font color="Green" title="E109">A12</font></i>: 
<font color="Maroon" title="c3">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">H</font> being   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span>;<br/>
<a NAME="E18:137"/><i><font color="Green" title="E110">A13</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></i>;<br/>
<a NAME="E19:137"/><b>then </b><i><font color="Green" title="E111">A14</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">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">S</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T31" title="FINSEQ_4:th.31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E20:137"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span>
 
<b>by </b><i><a class="txt" href="chord.html#E11:137"><i><font color="Green" title="E105">A7</font></i></a>, <a class="txt" href="chord.html#E13:137"><i><font color="Green" title="E107">A9</font></i></a>, <a class="txt" href="chord.html#E14:137"><i><font color="Green" title="E108">A10</font></i></a>, <a class="ref" href="chord.html#T16" target="_self" title="CHORD:th.16">Th16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">y</font> = <font color="Maroon" title="c5">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c7">H</font> <b>by </b><i><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/>
<a NAME="E22:137"/>
<font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 
<b>by </b><i><a class="txt" href="chord.html#E18:137"><i><font color="Green" title="E110">A13</font></i></a>, <a class="ref" href="finseq_4.html#T29" title="FINSEQ_4:th.29">FINSEQ_4:29</a></i>;<br/>
<a NAME="E23:137"/><b>then </b><i><font color="Green" title="E112">A15</font></i>: 
<font color="Maroon" title="c8">y</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 
<b>by </b><i><a class="txt" href="chord.html#E2:137"><i><font color="Green" title="E99">A1</font></i></a>, <a class="txt" href="chord.html#E19:137"><i><font color="Green" title="E111">A14</font></i></a>, <a class="ref" href="chord.html#D13" target="_self" title="CHORD:def.13">Def13</a></i>;<br/>
<a NAME="E24:137"/><i><font color="Green" title="E113">A16</font></i>: 
not <font color="Maroon" title="c2">S</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="chord.html#E12:137"><i><font color="Green" title="E106">A8</font></i></a>, <a class="ref" href="chord.html#T107" target="_self" title="CHORD:th.107">Th107</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">C</font> = <font color="Maroon" title="c3">P</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c7">H</font> <b>by </b><i><a class="txt" href="chord.html#E16:137"><i><font color="Green" title="E109">A12</font></i></a>, <a class="ref" href="chord.html#T23" target="_self" title="CHORD:th.23">Th23</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">C</font> = <font color="Maroon" title="c9">C</font> as   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c7">H</font> <b>by </b><i><a class="txt" href="chord.html#E4:137"><i><font color="Green" title="E101">A3</font></i></a>, <a class="ref" href="glib_001.html#T177" title="GLIB_001:th.177">GLIB_001:177</a></i>;<br/>
<a NAME="E27:137"/>
( not <font color="Maroon" title="c3">P</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c3">P</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> )
 
<b>by </b><i><a class="txt" href="chord.html#E3:137"><i><font color="Green" title="E100">A2</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E28:137"/><b>then </b>
( not <font color="Maroon" title="c10">C</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c10">C</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> )
 
<b>by </b><i><a class="ref" href="glib_001.html#T177" title="GLIB_001:th.177">GLIB_001:177</a></i>;<br/>
<a NAME="E29:137"/><b>then </b><i><font color="Green" title="E114">A17</font></i>: 
<font color="Maroon" title="c10">C</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>
 
<b>by </b><i><a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E30:137"/><i><font color="Green" title="E115">A18</font></i>: 
<font color="Maroon" title="c10">C</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
 
<b>by </b><i><a class="txt" href="chord.html#E3:137"><i><font color="Green" title="E100">A2</font></i></a>, <a class="ref" href="glib_001.html#T115" title="GLIB_001:th.115">GLIB_001:115</a></i>;<br/>
<a NAME="E31:137"/>
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="chord.html#E8:137"><i><font color="Green" title="E103">A5</font></i></a>, <a class="ref" href="glib_001.html#T99" title="GLIB_001:th.99">GLIB_001:99</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">b</font> being  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a> <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E33:137"/><i><font color="Green" title="E116">A19</font></i>: 
( <font color="Maroon" title="c11">a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c12">b</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="c10">C</font> )
 <b>and </b><br/><a NAME="E34:137"/><i><font color="Green" title="E117">A20</font></i>: 
( <font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">H</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">H</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>and </b><br/><a NAME="E35:137"/><i><font color="Green" title="E118">A21</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  holds <br/> not <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="chord.html#E29:137"><i><font color="Green" title="E114">A17</font></i></a>, <a class="txt" href="chord.html#E30:137"><i><font color="Green" title="E115">A18</font></i></a>, <a class="ref" href="chord.html#T55" target="_self" title="CHORD:th.55">Th55</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E37:137"/><i><font color="Green" title="E119">A22</font></i>: 
<font color="Maroon" title="c13">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="chord.html#E23:137"><i><font color="Green" title="E112">A15</font></i></a>, <a class="txt" href="chord.html#E34:137"><i><font color="Green" title="E117">A20</font></i></a>, <a class="ref" href="chord.html#T68" target="_self" title="CHORD:th.68">Th68</a></i>;<br/>
<a NAME="E38:137"/>
<font color="Maroon" title="c10">C</font> is <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>
 
<b>by </b><i><a class="txt" href="chord.html#E33:137"><i><font color="Green" title="E116">A19</font></i></a>, <a class="txt" href="chord.html#E34:137"><i><font color="Green" title="E117">A20</font></i></a>, <a class="txt" href="chord.html#E35:137"><i><font color="Green" title="E118">A21</font></i></a>, <a class="txt" href="chord.html#E37:137"><i><font color="Green" title="E119">A22</font></i></a>, <a class="ref" href="chord.html#D10" target="_self" title="CHORD:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E39:137"/>
<font color="Maroon" title="c3">P</font> is <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>
 <b>by </b><i><a class="txt" href="chord.html#E24:137"><i><font color="Green" title="E113">A16</font></i></a>, <a class="ref" href="chord.html#T87" target="_self" title="CHORD:th.87">Th87</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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