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<span class="kw">take </span><font color="Maroon" title="c1">G</font> =  the   <a href="scmyciel.html#V1" title="SCMYCIEL:attr.1">void</a>  <a href="scmyciel.html#NM1" title="SCMYCIEL:NM.1">SimpleGraph</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="c1">G</font> is  <a href="scmyciel.html#V6" title="SCMYCIEL:attr.6">with_finite_clique#</a> </span><br/>

<a NAME="E1:103_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmyciel.html#T20" target="_self" onmouseover="rs('scmyciel/T20')" onmouseout="rh()">Th20</a></span>;<br/>
<a NAME="E2:103_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">C</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="scmyciel.html#NM6" title="SCMYCIEL:NM.6">Clique</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="scmyciel.html#T48" target="_self" onmouseover="rs('scmyciel/T48')" onmouseout="rh()">Th48</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">C</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="scmyciel.html#D14" target="_self" onmouseover="rs('scmyciel/D14')" onmouseout="rh()">SCMYCIEL:def 14</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">D</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="scmyciel.html#NM6" title="SCMYCIEL:NM.6">Clique</a> of <font color="Maroon" title="c1">G</font> holds   <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Olive" title="b1">D</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Maroon" title="c2">C</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">D</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="scmyciel.html#NM6" title="SCMYCIEL:NM.6">Clique</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">  <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Maroon" title="c3">D</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Maroon" title="c2">C</font></span><br/>

<a NAME="E4:103_1_1"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T77" onmouseover="rs('zfmisc_1/T77')" onmouseout="rh()">ZFMISC_1:77</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:103_1_1"/>
 <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Maroon" title="c3">D</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Maroon" title="c2">C</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"> verum</span><br/>


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