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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: TOPREAL3:21</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">N</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b2">N</font></span>)</span><br/>  for <font color="Olive" title="b5">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Olive" title="b2">N</font></span>)</span>  st <font color="Olive" title="b3">p1</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="b5">u</font>,<font color="Olive" title="b1">r</font>) &amp; <font color="Olive" title="b4">p2</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="b5">u</font>,<font color="Olive" title="b1">r</font>) holds <br/> <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</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="b5">u</font>,<font color="Olive" title="b1">r</font>)</div></div>
