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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: YELLOW_8:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">P</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_8.html#K1" title="YELLOW_8:func.1">CofinTop</a> <font color="Olive" title="b1">X</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">P</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  iff ( <font color="Olive" title="b2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> or <font color="Olive" title="b2">P</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) )</div></div>
