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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: CONNSP_1:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">TS</font> being    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">K</font>, <font color="Olive" title="b3">L</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">TS</font>  st ( ( <font color="Olive" title="b2">K</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b3">L</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  ) or ( <font color="Olive" title="b2">K</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive" title="b3">L</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  ) ) holds <br/><font color="Olive" title="b2">K</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b3">L</font>,<font color="Olive" title="b3">L</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b2">K</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> </div></div>
