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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: SIMPLEX1:15</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="simplex0.html#NV10" title="SIMPLEX0:NV.10">with_empty_element</a>  <a href="simplex1.html#NM2" title="SIMPLEX1:NM.2">SimplicialComplex</a> of <font color="Olive" title="b1">V</font>  st <span class="p1"><a href="simplex1.html#K3" title="SIMPLEX1:func.3">|.</a><span class="default"><font color="Olive" title="b2">K</font></span><a href="simplex1.html#K3" title="SIMPLEX1:func.3">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b2">K</font> holds <br/> for <font color="Olive" title="b3">B</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>  st (  for <font color="Olive" title="b4">S</font> being   <a href="simplex0.html#NM5" title="SIMPLEX0:NM.5">Simplex</a> of <font color="Olive" title="b2">K</font>  st  not <font color="Olive" title="b4">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  holds <br/><font color="Olive" title="b3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <span class="p1">(<span class="default"><a href="simplex1.html#K1" title="SIMPLEX1:func.1">@</a> <font color="Olive" title="b4">S</font></span>)</span> ) holds <br/> <a href="simplex0.html#K11" title="SIMPLEX0:func.11">subdivision</a> (<font color="Olive" title="b3">B</font>,<font color="Olive" title="b2">K</font>) is    <a href="simplex1.html#M1" title="SIMPLEX1:mode.1">SubdivisionStr</a> of <font color="Olive" title="b2">K</font></div></div>
