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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th29</font></span>: <a NAME="T29"><span class="comment"><font color="firebrick">:: METRIC_2:29</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">VQv</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">M</font> <a href="metric_2.html#K2" title="METRIC_2:func.2">-neighbour</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">M</font> <a href="metric_2.html#K2" title="METRIC_2:func.2">-neighbour</a></span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> holds <br/> ( <font color="Olive" title="b2">VQv</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_2.html#K9" title="METRIC_2:func.9">set_in_rel</a> <font color="Olive" title="b1">M</font> iff  ex <font color="Olive" title="b3">V</font>, <font color="Olive" title="b4">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>  ex <font color="Olive" title="b5">v</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <br/>( <font color="Olive" title="b2">VQv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b3">V</font>,<font color="Olive" title="b4">Q</font>,<font color="Olive" title="b5">v</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Olive" title="b3">V</font>,<font color="Olive" title="b4">Q</font> <a href="metric_2.html#R4" title="METRIC_2:pred.4">is_dst</a> <font color="Olive" title="b5">v</font> ) )</div></div>
