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<span class="kw">let </span><font color="Maroon" title="c4">KA</font> be   <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">SC</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="c4">KA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">SC</font> <a href="simplex0.html#K7" title="SIMPLEX0:func.7">|</a> <font color="Maroon" title="c3">A</font> iff  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">KA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )</span><br/>

<a NAME="E1:93_1_1"/>
(  <a href="matroid0.html#K1" title="MATROID0:func.1">the_family_of</a> <font color="Maroon" title="c2">SC</font> is  <a href="finset_1.html#V5" title="FINSET_1:attr.5">finite-membered</a>  &amp; <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">SC</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">SC</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matroid0.html#D6" onmouseover="rs('matroid0/D6')" onmouseout="rh()">MATROID0:def 6</a>, <a class="ref" href="xboole_1.html#T17" onmouseover="rs('xboole_1/T17')" onmouseout="rh()">XBOOLE_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:93_1_1"/>
( <font color="Maroon" title="c4">KA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">SC</font> <a href="simplex0.html#K7" title="SIMPLEX0:func.7">|</a> <font color="Maroon" title="c3">A</font> iff  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">KA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D15" target="_self" onmouseover="rs('simplex0/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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