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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E28">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: SIMPLEX1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  <a href="simplex1.html#NM1" title="SIMPLEX1:NM.1">SimplicialComplexStr</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b2">K</font> is  <a href="simplex1.html#V2" title="SIMPLEX1:attr.2">simplex-join-closed</a>  iff  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">K</font>  st <font color="Olive" title="b3">A</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp; <font color="Olive" title="b4">B</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="rlaffin2.html#K1" title="RLAFFIN2:func.1">Int</a> <span class="p1">(<span class="default"><a href="simplex1.html#K1" title="SIMPLEX1:func.1">@</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="rlaffin2.html#K1" title="RLAFFIN2:func.1">Int</a> <span class="p1">(<span class="default"><a href="simplex1.html#K1" title="SIMPLEX1:func.1">@</a> <font color="Olive" title="b4">B</font></span>)</span> holds <br/><font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">B</font> )</div></div>
