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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: JORDAN1K:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">C</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b3">D</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">D</font> holds <br/> for <font color="Olive" title="b4">q</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="b1">n</font></span>)</span> holds   <a href="jordan1k.html#K5" title="JORDAN1K:func.5">dist</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b3">D</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="jordan1k.html#K5" title="JORDAN1K:func.5">dist</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">C</font>) <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1k.html#T41" target="_self" onmouseover="rs('jordan1k/T41')" onmouseout="rh()">Th41</a></span>;<br/></div></div>
