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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: PCOMPS_1:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">PM</font> being    <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> <br/>  for <font color="Olive" title="b2">V</font>, <font color="Olive" title="b3">W</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">PM</font>  st <font color="Olive" title="b2">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pcomps_1.html#K2" title="PCOMPS_1:func.2">Family_open_set</a> <font color="Olive" title="b1">PM</font> &amp; <font color="Olive" title="b3">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pcomps_1.html#K2" title="PCOMPS_1:func.2">Family_open_set</a> <font color="Olive" title="b1">PM</font> holds <br/><font color="Olive" title="b2">V</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pcomps_1.html#K2" title="PCOMPS_1:func.2">Family_open_set</a> <font color="Olive" title="b1">PM</font></div></div>
