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<div>:: <span class="kw">deftheorem </span>   defines <a href="sppol_1.html#R1" title="SPPOL_1:pred.1">is_extremal_in</a> <a onclick="hs(this)" href="javascript:()">SPPOL_1:def 1 : <br/></a><span> 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">p</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><br/>  for <font color="Olive" title="b3">P</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> holds <br/> ( <font color="Olive" title="b2">p</font> <a href="sppol_1.html#R1" title="SPPOL_1:pred.1">is_extremal_in</a> <font color="Olive" title="b3">P</font> iff ( <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">P</font> &amp; (  for <font color="Olive" title="b4">p1</font>, <font color="Olive" title="b5">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="b1">n</font></span>)</span>  st <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b4">p1</font>,<font color="Olive" title="b5">p2</font>) &amp;  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b4">p1</font>,<font color="Olive" title="b5">p2</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">P</font> &amp;  not <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p1</font> holds <br/><font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">p2</font> ) ) );<br/></span></div>
