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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="chord.html#V6" title="CHORD:attr.6">chordal</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"> for <font color="Olive" title="b1">g</font> being <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>  <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">H</font> holds <br/><font color="Olive" title="b1">g</font> is  <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>  <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c2">H</font></span><br/><b>let </b><font color="Maroon" title="c3">g</font> be  <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>  <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c1">G</font>; <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> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c3">g</font> is  <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>  <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c2">H</font> )</span><br/>



<b>assume </b><a NAME="E1:135"/><i><font color="Green" title="E99">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">g</font> is  <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>  <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c2">H</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">h</font> = <font color="Maroon" title="c3">g</font> as    <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c2">H</font> <b>by </b><i><a class="txt" href="#E1:135"><i><font color="Green" title="E99">A1</font></i></a>, <a class="ref" href="chord.html#T106" target="_self" title="CHORD:th.106">Th106</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a> <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">n</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="c4">h</font> implies for <font color="Olive" title="b1">Hf</font> being  <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c2">H</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <font color="Maroon" title="c5">n</font></span>)</span><br/> for <font color="Olive" title="b2">vh</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">Hf</font>  st <font color="Olive" title="b2">vh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> holds <br/><font color="Olive" title="b2">vh</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> )</span><br/><b>assume </b><a NAME="E1:135_1"/><i><font color="Green" title="E100">A2</font></i>: 
<font color="Maroon" title="c5">n</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="c4">h</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Hf</font> being  <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c2">H</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <font color="Maroon" title="c5">n</font></span>)</span><br/> for <font color="Olive" title="b2">vh</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">Hf</font>  st <font color="Olive" title="b2">vh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> holds <br/><font color="Olive" title="b2">vh</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/><b>let </b><font color="Maroon" title="c6">Hf</font> be   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c2">H</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <font color="Maroon" title="c5">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">vh</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c6">Hf</font>  st <font color="Olive" title="b1">vh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> holds <br/><font color="Olive" title="b1">vh</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/><b>let </b><font color="Maroon" title="c7">vh</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c6">Hf</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">vh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c7">vh</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> )</span><br/><b>assume </b><a NAME="E2:135_1"/><i><font color="Green" title="E101">A3</font></i>: 
<font color="Maroon" title="c7">vh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">vh</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/><a NAME="E3:135_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <font color="Maroon" title="c5">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:135"><i><font color="Green" title="E99">A1</font></i></a>, <a class="ref" href="glib_000.html#T93" title="GLIB_000:th.93">GLIB_000:93</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c8">Gf</font> = <font color="Maroon" title="c6">Hf</font> as   <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="c3">g</font> <a href="chord.html#K4" title="CHORD:func.4">.followSet</a> <font color="Maroon" title="c5">n</font></span>)</span> <b>by </b><i><a class="txt" href="#E1:135"><i><font color="Green" title="E99">A1</font></i></a>, <a class="ref" href="glib_000.html#T98" title="GLIB_000:th.98">GLIB_000:98</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">vg</font> = <font color="Maroon" title="c7">vh</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c8">Gf</font> ;<br/><a NAME="E6:135_1"/>
<font color="Maroon" title="c9">vg</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 <b>by </b><i><a class="txt" href="#E1:135_1"><i><font color="Green" title="E100">A2</font></i></a>, <a class="txt" href="#E2:135_1"><i><font color="Green" title="E101">A3</font></i></a>, <a class="ref" href="chord.html#D13" target="_self" title="CHORD:def.13">Def13</a></i>;<br/><b>hence </b><a NAME="E7:135_1"/>
<font color="Maroon" title="c7">vh</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 ; <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>
<b>hence </b><a NAME="E4:135"/>
<font color="Maroon" title="c3">g</font> is  <a href="chord.html#V7" title="CHORD:attr.7">perfect</a>  <a href="chord.html#M3" title="CHORD:mode.3">VertexScheme</a> of <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="chord.html#D13" target="_self" title="CHORD:def.13">Def13</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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