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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: SIMPLEX0:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">KX</font> being    <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">i</font> being   <a href="int_1.html#V2" title="INT_1:attr.2">dim-like</a>   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">number</a>   st <font color="Olive" title="b2">KX</font> is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  &amp;  <a href="simplex0.html#K8" title="SIMPLEX0:func.8">Skeleton_of</a> (<font color="Olive" title="b2">KX</font>,<font color="Olive" title="b3">i</font>) is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp;  not <font color="Olive" title="b2">KX</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  holds <br/><font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="simplex0.html#K9" title="SIMPLEX0:func.9">-</a> 1</div></div>
