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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E54">Th63</font></span>: <a NAME="T63"><span class="comment"><font color="firebrick">:: SIMPLEX0:63</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">P</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b4">n</font>, <font color="Olive" title="b5">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds   <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b5">k</font></span>)</span>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">KX</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> (<font color="Olive" title="b4">n</font>,<font color="Olive" title="b3">P</font>,<span class="p1">(<span class="default"><a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> (<font color="Olive" title="b5">k</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">KX</font>)</span>)</span>)</div></div>
