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<div>:: <span class="kw">deftheorem </span>   defines <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <a onclick="hs(this)" href="javascript:()">JORDAN6:def 10 : <br/></a><span> for <font color="Olive" title="b1">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> 2</span>)</span><br/>  for <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</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> 2</span>)</span> holds <br/> (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>,<font color="Olive" title="b1">P</font> iff ( ( <font color="Olive" title="b2">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b3">q2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Olive" title="b1">P</font> &amp;  not <font color="Olive" title="b3">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Olive" title="b1">P</font> ) or ( <font color="Olive" title="b2">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b3">q2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Olive" title="b1">P</font> &amp;  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Olive" title="b1">P</font>, <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Olive" title="b1">P</font>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Olive" title="b1">P</font> ) or ( <font color="Olive" title="b2">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b3">q2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Olive" title="b1">P</font> &amp;  not <font color="Olive" title="b3">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Olive" title="b1">P</font> &amp;  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>, <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Olive" title="b1">P</font>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Olive" title="b1">P</font>, <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Olive" title="b1">P</font> ) ) );<br/></span></div>
