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<b>let </b><font color="Maroon">P</font> be  <a href="jordan1.html#V1">convex</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>, <font color="Maroon">Q</font> be  <a href="jordan1.html#V1">convex</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">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>; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan1.html#D1">JORDAN1:def 1</a><br/><b>let </b><font color="Maroon">q</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="E1:8"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font> )
 ;<br/>

<a NAME="E2:8"/><b>then </b>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:8"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="jordan1.html#D1">JORDAN1:def 1</a></i>;<br/>
<a NAME="E4:8"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font>
 
<b>by </b><i><a class="ref" href="jordan1.html#D1">JORDAN1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:8"/>
 <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>


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