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<div><span class="kw">theorem </span><a NAME="T14"><span class="comment"><font color="firebrick">:: JORDAN5C:14</font></span><br/></a><div class="add"> 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">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">q1</font>, <font color="Olive" title="b5">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>  st <font color="Olive" title="b1">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b4">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b5">q2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b4">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">q2</font> &amp;  not <!--HUMANRECFAILED-->(  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b4">q1</font>,<font color="Olive" title="b5">q2</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> &amp;  not  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b5">q2</font>,<font color="Olive" title="b4">q1</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> ) holds <br/>(  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b5">q2</font>,<font color="Olive" title="b4">q1</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> &amp;  not  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b4">q1</font>,<font color="Olive" title="b5">q2</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> )</div></div>
