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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th4</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: TOPREAL9:6</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   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a><br/>  for <font color="Olive" title="b3">z1</font>, <font color="Olive" title="b4">z2</font>, <font color="Olive" title="b5">z3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">M</font>  st <font color="Olive" title="b3">z1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">z2</font> &amp; <font color="Olive" title="b3">z1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">cl_Ball</a> (<font color="Olive" title="b5">z3</font>,<font color="Olive" title="b1">r</font>) &amp; <font color="Olive" title="b4">z2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">cl_Ball</a> (<font color="Olive" title="b5">z3</font>,<font color="Olive" title="b1">r</font>) holds <br/><font color="Olive" title="b1">r</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> </div></div>
