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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <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"> ( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> implies for <font color="Olive" title="b1">u1</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">u2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u2</font> &amp; <font color="Olive" title="b1">u1</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> holds <br/><font color="Olive" title="b2">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> )</span><br/>

<b>assume </b><a NAME="E1:78"/><i><font color="Green" title="E63">A1</font></i>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</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">u1</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">u2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u2</font> &amp; <font color="Olive" title="b1">u1</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> holds <br/><font color="Olive" title="b2">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/>

<b>let </b><font color="Maroon" title="c3">u1</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</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">u2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u2</font> &amp; <font color="Maroon" title="c3">u1</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> holds <br/><font color="Olive" title="b1">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/><b>let </b><font color="Maroon" title="c4">u2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</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">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u2</font> &amp; <font color="Maroon" title="c3">u1</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> implies <font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> )</span><br/>



<b>assume </b><a NAME="E2:78"/><i><font color="Green" title="E64">A2</font></i>: 
<font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">u1</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> or <font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> )</span><br/>

<b>assume </b><a NAME="E3:78"/><i><font color="Green" title="E65">A3</font></i>: 
<font color="Maroon" title="c3">u1</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"> <font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="78_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:78_1_1"/>
( <font color="Maroon" title="c1">G1</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="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c1">G1</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="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="78_1_1_1"><b>suppose </b></a><a NAME="E1:78_1_1_1"/>
<font color="Maroon" title="c1">G1</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="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/><div class="add"><a NAME="E2:78_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">G2</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="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="chord.html#E1:78"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="chord.html#E2:78"><i><font color="Green" title="E64">A2</font></i></a>, <a class="ref" href="chord.html#T51" target="_self" title="CHORD:th.51">Th51</a></i>;<br/><b>hence </b><a NAME="E3:78_1_1_1"/>
<font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 <b>by </b><i><a class="ref" href="chord.html#D7" target="_self" title="CHORD:def.7">Def7</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="78_1_1_2"><b>suppose </b></a><a NAME="E1:78_1_1_2"/><i><font color="Green" title="E66">A4</font></i>: 
<font color="Maroon" title="c1">G1</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="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a></span><br/><div class="add"><b>consider </b><font color="Maroon" title="c5">H1</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/><a NAME="E3:78_1_1_2"/>
<font color="Maroon" title="c5">H1</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a>
 <b>by </b><i><a class="txt" href="chord.html#E3:78"><i><font color="Green" title="E65">A3</font></i></a>, <a class="txt" href="chord.html#E1:78_1_1_2"><i><font color="Green" title="E66">A4</font></i></a>, <a class="ref" href="chord.html#D7" target="_self" title="CHORD:def.7">Def7</a></i>;<br/><a NAME="E4:78_1_1_2"/><b>then </b>
for <font color="Olive" title="b1">H2</font> being   <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Olive" title="b1">H2</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a>
 <b>by </b><i><a class="txt" href="chord.html#E1:78"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="chord.html#E2:78"><i><font color="Green" title="E64">A2</font></i></a>, <a class="ref" href="chord.html#T59" target="_self" title="CHORD:th.59">Th59</a>, <a class="ref" href="chord.html#T62" target="_self" title="CHORD:th.62">Th62</a></i>;<br/><b>hence </b><a NAME="E5:78_1_1_2"/>
<font color="Maroon" title="c4">u2</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 <b>by </b><i><a class="ref" href="chord.html#D7" target="_self" title="CHORD:def.7">Def7</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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:78"/>
<font color="Maroon" title="c4">u2</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/>


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