<?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#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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">given </span><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><span class="kw"> such that </span><a NAME="E2:135"/><span class="lab"><font color="Green" title="E99">A1</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<a NAME="E3:135"/><span class="lab"><font color="Green" title="E100">A2</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></span>;<br/>
<span class="kw">let </span><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>; <span class="comment"><font color="firebrick">:: according to </font></span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:135"/><span class="lab"><font color="Green" title="E101">A3</font></span>: 
<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
 <span class="kw">and </span><br/><a NAME="E5:135"/><span class="lab"><font color="Green" title="E102">A4</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E6:135"/>
 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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:135"/><span class="lab"><font color="Green" title="E103">A5</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E9:135"/><span class="lab"><font color="Green" title="E104">A6</font></span>: 
 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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:135"><span class="lab"><font color="Green" title="E100">A2</font></span></a>, <a class="ref" href="chord.html#T15" target="_self" title="CHORD:th.15">Th15</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:135"><span class="lab"><font color="Green" title="E103">A5</font></span></a></span>;<br/>
<span class="kw">set </span><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/>
<span class="kw">set </span><font color="Maroon" title="c7">H</font> =  the   <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="E11:135"/><span class="lab"><font color="Green" title="E105">A7</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></span>;<br/>
<a NAME="E12:135"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A8</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T20" title="FINSEQ_4:th.20">FINSEQ_4:20</a></span>;<br/>
<a NAME="E13:135"/><span class="lab"><font color="Green" title="E107">A9</font></span>: 
<font color="Maroon" title="c2">S</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></span>;<br/>
<a NAME="E14:135"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:135"><span class="lab"><font color="Green" title="E105">A7</font></span></a>, <a class="txt" href="#E12:135"><span class="lab"><font color="Green" title="E106">A8</font></span></a>, <a class="ref" href="chord.html#T16" target="_self" title="CHORD:th.16">Th16</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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  the   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/>
<a NAME="E16:135"/><span class="lab"><font color="Green" title="E108">A10</font></span>: 
 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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:135"><span class="lab"><font color="Green" title="E105">A7</font></span></a>, <a class="ref" href="chord.html#T107" target="_self" title="CHORD:th.107">Th107</a>, <a class="ref" href="finseq_4.html#T21" title="FINSEQ_4:th.21">FINSEQ_4:21</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c9">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="c9">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/><span class="kw">assume </span><a NAME="E1:135_1"/><span class="lab"><font color="Green" title="E109">A11</font></span>: 
<font color="Maroon" title="c9">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">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/><span class="kw">reconsider </span><font color="Maroon" title="c10">z</font> = <font color="Maroon" title="c9">y</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:135_1"><span class="lab"><font color="Green" title="E109">A11</font></span></a></span>;<br/><a NAME="E3:135_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="c10">z</font> <a href="chord.html#K3" title="CHORD:func.3">..</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:135"><span class="lab"><font color="Green" title="E104">A6</font></span></a>, <a class="txt" href="#E1:135_1"><span class="lab"><font color="Green" title="E109">A11</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:135_1"/>
<font color="Maroon" title="c9">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E11:135"><span class="lab"><font color="Green" title="E105">A7</font></span></a>, <a class="txt" href="#E12:135"><span class="lab"><font color="Green" title="E106">A8</font></span></a>, <a class="txt" href="#E13:135"><span class="lab"><font color="Green" title="E107">A9</font></span></a>, <a class="ref" href="chord.html#T16" target="_self" title="CHORD:th.16">Th16</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>
<a NAME="E18:135"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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  the   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:135"><span class="lab"><font color="Green" title="E108">A10</font></span></a>, <a class="ref" href="chord.html#T23" target="_self" title="CHORD:th.23">Th23</a></span>;<br/>
<span class="kw">reconsider </span><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  the   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:135"><span class="lab"><font color="Green" title="E102">A4</font></span></a>, <a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></span>;<br/>
<a NAME="E21:135"/><span class="lab"><font color="Green" title="E109">A12</font></span>: 
<font color="Maroon" title="c10">C</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:135"><span class="lab"><font color="Green" title="E102">A4</font></span></a>, <a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></span>;<br/>
<a NAME="E22:135"/><span class="lab"><font color="Green" title="E110">A13</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:135"><span class="lab"><font color="Green" title="E103">A5</font></span></a>, <a class="ref" href="glib_001.html#T98" title="GLIB_001:th.98">GLIB_001:98</a></span>;<br/>
<a NAME="E23:135"/><span class="lab"><font color="Green" title="E111">A14</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D12" target="_self" title="CHORD:def.12">Def12</a></span>;<br/>
<a NAME="E24:135"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A15</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T19" title="FINSEQ_4:th.19">FINSEQ_4:19</a></span>;<br/>
<a NAME="E25:135"/>
 not <font color="Maroon" title="c10">C</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:135"><span class="lab"><font color="Green" title="E102">A4</font></span></a>, <a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></span>;<br/>
<a NAME="E26:135"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A16</font></span>: 
<font color="Maroon" title="c10">C</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="#E21:135"><span class="lab"><font color="Green" title="E109">A12</font></span></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></span>;<br/>
<a NAME="E27:135"/>
<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
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:135"><span class="lab"><font color="Green" title="E101">A3</font></span></a>, <a class="ref" href="glib_001.html#T114" title="GLIB_001:th.114">GLIB_001:114</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E29:135"/><span class="lab"><font color="Green" title="E114">A17</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E30:135"/><span class="lab"><font color="Green" title="E115">A18</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E31:135"/><span class="lab"><font color="Green" title="E116">A19</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E32:135"/><span class="lab"><font color="Green" title="E117">A20</font></span>: 
<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>  the   <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> <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>
 <span class="kw">and </span><br/><a NAME="E33:135"/><span class="lab"><font color="Green" title="E118">A21</font></span>: 
<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>  the   <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> <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>
 <span class="kw">and </span><br/><a NAME="E34:135"/><span class="lab"><font color="Green" title="E119">A22</font></span>: 
 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>, the   <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:135"><span class="lab"><font color="Green" title="E113">A16</font></span></a>, <a class="txt" href="#E22:135"><span class="lab"><font color="Green" title="E110">A13</font></span></a>, <a class="ref" href="chord.html#T55" target="_self" title="CHORD:th.55">Th55</a></span>;<br/>
<a NAME="E35:135"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:135"><span class="lab"><font color="Green" title="E111">A14</font></span></a>, <a class="ref" href="finseq_4.html#T21" title="FINSEQ_4:th.21">FINSEQ_4:21</a></span>;<br/>
<a NAME="E36:135"/><span class="kw">then </span>
<font color="Maroon" title="c8">y</font> is  <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:135"><span class="lab"><font color="Green" title="E99">A1</font></span></a>, <a class="txt" href="#E24:135"><span class="lab"><font color="Green" title="E112">A15</font></span></a>, <a class="ref" href="chord.html#D13" target="_self" title="CHORD:def.13">Def13</a></span>;<br/>
<a NAME="E37:135"/><span class="kw">then </span>
 ex <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="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>, the   <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:135"><span class="lab"><font color="Green" title="E116">A19</font></span></a>, <a class="txt" href="#E32:135"><span class="lab"><font color="Green" title="E117">A20</font></span></a>, <a class="txt" href="#E33:135"><span class="lab"><font color="Green" title="E118">A21</font></span></a>, <a class="ref" href="chord.html#T68" target="_self" title="CHORD:th.68">Th68</a></span>;<br/>
<a NAME="E38:135"/><span class="kw">then </span>
<font color="Maroon" title="c10">C</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="#E29:135"><span class="lab"><font color="Green" title="E114">A17</font></span></a>, <a class="txt" href="#E30:135"><span class="lab"><font color="Green" title="E115">A18</font></span></a>, <a class="txt" href="#E31:135"><span class="lab"><font color="Green" title="E116">A19</font></span></a>, <a class="txt" href="#E34:135"><span class="lab"><font color="Green" title="E119">A22</font></span></a>, <a class="ref" href="chord.html#D10" target="_self" title="CHORD:def.10">Def10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E39:135"/>
<font color="Maroon" title="c3">P</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="#E16:135"><span class="lab"><font color="Green" title="E108">A10</font></span></a>, <a class="ref" href="chord.html#T87" target="_self" title="CHORD:th.87">Th87</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>
