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<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>let </b><font color="Maroon">p1</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">p2</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">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><b>that </b><br/><a NAME="E1:83"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">p1</font>,<font color="Maroon">p2</font> <a href="sppol_2.html#R1" target="_self">split</a> <font color="Maroon">P</font>
 <b>and </b><br/><a NAME="E2:83"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p2</font> )
 ;<br/>

<a NAME="E3:83"/>
<font color="Maroon">p2</font>,<font color="Maroon">p1</font> <a href="sppol_2.html#R1" target="_self">split</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="sppol_2.html#T15" target="_self">Th15</a>, <a class="ref" href="sppol_2.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E4:83"/><b>then </b>
<font color="Maroon">p2</font>,<font color="Maroon">q</font> <a href="sppol_2.html#R1" target="_self">split</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="sppol_2.html#T18" target="_self">Th18</a>, </i>;<br/>
<b>hence </b><a NAME="E5:83"/>
<font color="Maroon">q</font>,<font color="Maroon">p2</font> <a href="sppol_2.html#R1" target="_self">split</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="sppol_2.html#T13" target="_self">Th13</a></i>;<br/>


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