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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: JORDAN20:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</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="b2">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">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> 2</span>)</span><br/>  for <font color="Olive" title="b5">e</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">P</font> <a href="topreal4.html#R1" title="TOPREAL4:pred.1">is_S-P_arc_joining</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b2">p1</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b4">p</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">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp;  not <font color="Olive" title="b4">p</font> <a href="jordan20.html#R1" title="JORDAN20:pred.1">is_Lin</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b5">e</font> holds <br/><font color="Olive" title="b4">p</font> <a href="jordan20.html#R2" title="JORDAN20:pred.2">is_Rin</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b5">e</font></div></div>
