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<b>let </b><font color="Maroon">p</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>let </b><font color="Maroon">R</font> be   <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">P</font> be   <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>assume </b><a NAME="E1:33"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">R</font> <a href="topreal4.html#NR3" target="_self">is_Region</a>  &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> &amp; <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">q</font> where <font color="Olive">q</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> : ( <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> or  ex <font color="Olive">P1</font> being  <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> st <br/>( <font color="Olive">P1</font> <a href="topreal4.html#R1" target="_self">is_S-P_arc_joining</a> <font color="Maroon">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">P1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font> ) ) </span>}</span>  )
 ;<br/>

<b>hence </b><a NAME="E2:33"/>
<font color="Maroon">R</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E3:33"/>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font>
 <b>by </b><i>, </i>;<br/>


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