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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: SIMPLEX0:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">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="b3">S</font> being    <a href="simplex0.html#M3" title="SIMPLEX0:mode.3">Simplex</a> of <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">K</font>  st  not <font color="Olive" title="b3">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  holds <br/><font color="Olive" title="b1">i</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> </div></div>
