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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: METRIC_2:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font> being   <a href="metric_1.html#NM2" title="METRIC_1:NM.2">PseudoMetricSpace</a><br/>  for <font color="Olive" title="b2">V</font>, <font color="Olive" title="b3">Q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">M</font> <a href="metric_2.html#K2" title="METRIC_2:func.2">-neighbour</a> <br/>  for <font color="Olive" title="b4">v</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( <font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">Q</font> <a href="metric_2.html#R4" title="METRIC_2:pred.4">is_dst</a> <font color="Olive" title="b4">v</font> iff  ex <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">M</font> st <br/>( <font color="Olive" title="b5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">V</font> &amp; <font color="Olive" title="b6">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">Q</font> &amp;  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v</font> ) )</div></div>
