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<b>let </b><font color="Maroon">P</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">q1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<font color="Maroon">P</font> <a href="topreal2.html#NR1" target="_self">is_simple_closed_curve</a> 
 ;<br/>

<a NAME="E3:11"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">q1</font>,<font color="Maroon">q1</font>,<font color="Maroon">P</font>
 
<b>by </b><i>, <a class="ref" href="jordan6.html#T71">JORDAN6:71</a></i>;<br/>
<a NAME="E4:11"/><b>then </b>
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">p1</font> where <font color="Olive">p1</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">q1</font>,<font color="Olive">p1</font>,<font color="Maroon">P</font> or ( <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Olive">p1</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">P</font> ) ) </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E5:11"/>
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="jordan7.html#K1" target="_self">Segment</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">P</font></span>)</span>,<font color="Maroon">P</font>
 <b>by </b><i/>;<br/>


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