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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="scmyciel.html#V6" title="SCMYCIEL:attr.6">with_finite_clique#</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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">H</font> implies  <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c1">G</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c2">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:110"/><span class="lab"><font color="Green" title="E70">A1</font></span>: 
<font color="Maroon" title="c1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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">  <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c1">G</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c2">H</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">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><span class="kw"> such that </span><br/><a NAME="E3:110"/><span class="lab"><font color="Green" title="E71">A2</font></span>: 
 <a href="scmyciel.html#K2" title="SCMYCIEL:func.2">order</a> <font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmyciel.html#D15" target="_self" onmouseover="rs('scmyciel/D15')" onmouseout="rh()">Def15</a></span>;<br/>
<a NAME="E4:110"/>
<font color="Maroon" title="c3">D</font> is   <a href="scmyciel.html#NM6" title="SCMYCIEL:NM.6">Clique</a> of <font color="Maroon" title="c2">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:110"/>
 <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c1">G</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="scmyciel.html#K8" title="SCMYCIEL:func.8">clique#</a> <font color="Maroon" title="c2">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:110"><span class="lab"><font color="Green" title="E71">A2</font></span></a>, <a class="ref" href="scmyciel.html#D15" target="_self" onmouseover="rs('scmyciel/D15')" onmouseout="rh()">Def15</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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