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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> <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/>



<span class="kw">assume </span><a NAME="E1:129"/><span class="lab"><font color="Green" title="E96">A1</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129"><span class="lab"><font color="Green" title="E96">A1</font></span></a>, <a class="ref" href="chord.html#T106" target="_self" onmouseover="rs('chord/T106')" onmouseout="rh()">Th105</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="129_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">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> holds <br/> for <font color="Olive" title="b2">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="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b3">vh</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b2">Hf</font>  st <font color="Olive" title="b3">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="Olive" title="b1">n</font> holds <br/><font color="Olive" title="b3">vh</font> is  <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">n</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">assume </span><a NAME="E1:129_1"/><span class="lab"><font color="Green" title="E97">A2</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">assume </span><a NAME="E2:129_1"/><span class="lab"><font color="Green" title="E98">A3</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E3:129_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.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#K21" title="GLIB_000:func.21">.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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129"><span class="lab"><font color="Green" title="E96">A1</font></span></a>, <a class="ref" href="glib_000.html#T90" onmouseover="rs('glib_000/T90')" onmouseout="rh()">GLIB_000:90</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129"><span class="lab"><font color="Green" title="E96">A1</font></span></a>, <a class="ref" href="glib_000.html#T95" onmouseover="rs('glib_000/T95')" onmouseout="rh()">GLIB_000:95</a></span>;<br/><span class="kw">reconsider </span><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="E6:129_1"/>
<font color="Maroon" title="c9">vg</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="#E1:129_1"><span class="lab"><font color="Green" title="E97">A2</font></span></a>, <a class="txt" href="#E2:129_1"><span class="lab"><font color="Green" title="E98">A3</font></span></a>, <a class="ref" href="chord.html#D13" target="_self" onmouseover="rs('chord/D13')" onmouseout="rh()">Def13</a></span>;<br/><span class="kw">hence </span><a NAME="E7:129_1"/>
<font color="Maroon" title="c7">vh</font> is  <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<span class="kw">hence </span><a NAME="E4:129"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D13" target="_self" onmouseover="rs('chord/D13')" onmouseout="rh()">Def13</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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