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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: HAUSDORF:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</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="pcomps_1.html#K3" title="PCOMPS_1:func.3">TopSpaceMetr</a> <font color="Olive" title="b1">M</font></span>)</span><br/>  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">P</font> holds <br/><span class="p1">(<span class="default"><a href="weierstr.html#K6" title="WEIERSTR:func.6">dist_min</a> <font color="Olive" title="b2">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </div></div>
