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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th63</font></span>: <a NAME="T63"><span class="comment"><font color="firebrick">:: TOPGEN_4:63</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Olive" title="b1">T</font>  ex <font color="Olive" title="b3">Y</font> being   <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a>   <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a>   <a href="topgen_4.html#V3" title="TOPGEN_4:attr.3">closed_for_countable_unions</a>  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Olive" title="b1">T</font> st <br/>( <font color="Olive" title="b2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Y</font> &amp; (  for <font color="Olive" title="b4">Z</font> being   <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a>   <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a>   <a href="topgen_4.html#V3" title="TOPGEN_4:attr.3">closed_for_countable_unions</a>  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">Z</font> holds <br/><font color="Olive" title="b3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">Z</font> ) )</div></div>
