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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: JORDAN20:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q1</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> 2</span>)</span><br/>  for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font>, <font color="Olive" title="b5">q1</font>, <font color="Olive" title="b6">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="b3">p1</font>,<font color="Olive" title="b4">p2</font> &amp; <font color="Olive" title="b2">Q1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">q2</font> &amp;  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">q2</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font> &amp; <font color="Olive" title="b2">Q1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">P</font> holds <br/><font color="Olive" title="b2">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">q2</font>)</div></div>
