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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th13</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: METRIC_1:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">M</font> being    <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> <br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">M</font> holds <br/> ( <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">Sphere</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">r</font>) iff (  not <font color="Olive" title="b2">M</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  <a href="metric_1.html#K1" title="METRIC_1:func.1">dist</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> ) )</div></div>
