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<div>:: <span class="kw">deftheorem </span>   defines <a href="jordan24.html#R1" title="JORDAN24:pred.1">realize-max-dist-in</a> <a onclick="hs(this)" href="javascript:()">JORDAN24:def 1 : <br/></a><span> for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">A</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><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</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 <br/> ( <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="jordan24.html#R1" title="JORDAN24:pred.1">realize-max-dist-in</a> <font color="Olive" title="b2">A</font> iff ( <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; (  for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</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="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b6">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> holds <br/> <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font>) ) ) );<br/></span></div>
