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<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2">finite</a> <a href="chord.html#V6" target="_self">chordal</a> <a href="glib_000.html#NM2">_Graph</a>, <font color="Maroon">H</font> be  <a href="glib_000.html#V2">finite</a> <a href="chord.html#V6" target="_self">chordal</a> <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">g</font> be  <a href="chord.html#V7" target="_self">perfect</a>  <a href="chord.html#M3" target="_self">VertexScheme</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:136"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">H</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">h</font> = <font color="Maroon">g</font> as    <a href="chord.html#M3" target="_self">VertexScheme</a> of <font color="Maroon">H</font> <b>by </b><i><a class="ref" href="chord.html#T21" target="_self">Th21</a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="136_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">zero</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:136_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font>
 ;<br/><b>let </b><font color="Maroon">Hf</font> be   <a href="glib_000.html#NM5">inducedSubgraph</a> of <font color="Maroon">H</font>,<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="chord.html#K4" target="_self">.followSet</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">vh</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">Hf</font>;<br/><b>assume </b><a NAME="E2:136_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">vh</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E3:136_1"/>
<font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="chord.html#K4" target="_self">.followSet</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="chord.html#K4" target="_self">.followSet</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="chord.html#T21" target="_self">Th21</a>, <a class="ref" href="glib_000.html#T93">GLIB_000:93</a></i>;<br/><b>then reconsider </b><font color="Maroon">Gf</font> = <font color="Maroon">Hf</font> as   <a href="glib_000.html#NM5">inducedSubgraph</a> of <font color="Maroon">G</font>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="chord.html#K4" target="_self">.followSet</a> <font color="Maroon">n</font></span>)</span> <b>by </b><i><a class="ref" href="chord.html#T21" target="_self">Th21</a>, <a class="ref" href="glib_000.html#T98">GLIB_000:98</a></i>;<br/><b>reconsider </b><font color="Maroon">vg</font> = <font color="Maroon">vh</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">Gf</font> ;<br/><a NAME="E6:136_1"/>
<font color="Maroon">vg</font> is <a href="chord.html#V3" target="_self">simplicial</a>
 <b>by </b><i><a class="ref" href="chord.html#T22" target="_self">Th22</a>, <a class="ref" href="chord.html#T23" target="_self">Th23</a>, </i>;<br/><b>hence </b><a NAME="E7:136_1"/>
<font color="Maroon">vh</font> is <a href="chord.html#V3" target="_self">simplicial</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:136"/>
<font color="Maroon">g</font> is  <a href="chord.html#V7" target="_self">perfect</a>  <a href="chord.html#M3" target="_self">VertexScheme</a> of <font color="Maroon">H</font>
 <b>by </b><i/>;<br/>


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