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<div><span class="kw">theorem </span><a NAME="T50"><span class="comment"><font color="firebrick">:: SIMPLEX0:50</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">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="b4">S</font> being    <a href="simplex0.html#M3" title="SIMPLEX0:mode.3">Simplex</a> of <font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">K</font>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="simplex0.html#K6" title="SIMPLEX0:func.6">degree</a> <font color="Olive" title="b3">K</font> holds <br/>( <font color="Olive" title="b1">X</font> is    <a href="simplex0.html#M4" title="SIMPLEX0:mode.4">Face</a> of <font color="Olive" title="b4">S</font> iff  ex <font color="Olive" title="b5">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">S</font> &amp; <font color="Olive" title="b4">S</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b5">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> ) )</div></div>
