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<div><span class="kw">theorem </span><a NAME="T48"><span class="comment"><font color="firebrick">:: SIMPLEX0:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   non  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>   <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  <a href="simplex0.html#NM1" title="SIMPLEX0:NM.1">SimplicialComplexStr</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="simplex0.html#NM5" title="SIMPLEX0:NM.5">Simplex</a> of <font color="Olive" title="b1">K</font> holds  <font color="Olive" title="b2">S</font> is    <a href="simplex0.html#M3" title="SIMPLEX0:mode.3">Simplex</a> of <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> 1,<font color="Olive" title="b1">K</font></div></div>
