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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: PCOMPS_1:27</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">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">PM</font><br/>  for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">PM</font> is  <a href="metric_1.html#V9" title="METRIC_1:attr.9">triangle</a>  &amp; <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b4">r</font>) holds <br/> ex <font color="Olive" title="b5">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b5">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b3">y</font>,<font color="Olive" title="b5">p</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b4">r</font>) )</div></div>
