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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">:: PRE_TOPC:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b3">p</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font> holds <br/>( <font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b2">A</font> iff  for <font color="Olive" title="b4">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b4">C</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">C</font> holds <br/><font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">C</font> )</div></div>
