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<div><span class="kw">theorem </span><a NAME="T28"><span class="comment"><font color="firebrick">:: PCOMPS_1:28</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">r</font>, <font color="Olive" title="b3">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font>, <font color="Olive" title="b6">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">PM</font>  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="b5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b2">r</font>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b6">z</font>,<font color="Olive" title="b3">p</font>)</span>)</span> holds <br/> ex <font color="Olive" title="b7">q</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>(  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b5">y</font>,<font color="Olive" title="b7">q</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="b4">x</font>,<font color="Olive" title="b2">r</font>) &amp;  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b5">y</font>,<font color="Olive" title="b7">q</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="b6">z</font>,<font color="Olive" title="b3">p</font>) )</div></div>
