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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th50</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: JORDAN1K:50</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">A</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">p</font>, <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>  st <font color="Olive" title="b4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> holds <br/> <a href="jordan1k.html#K5" title="JORDAN1K:func.5">dist</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">A</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font>)</div></div>
