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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>, <font color="Maroon">Q</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>, <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>assume </b><a NAME="E1:10"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">P</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">P</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> )
 ;<br/>

<a NAME="E2:10"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">P</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E3:10"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 
<b>by </b><i>, <a class="ref" href="topreal1.html#T4">TOPREAL1:4</a></i>;<br/>
<b>hence </b><a NAME="E4:10"/>
(  <a href="jordan5c.html#K1" target="_self">First_Point</a> <font color="Maroon">P</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp;  <a href="jordan5c.html#K2" target="_self">Last_Point</a> <font color="Maroon">P</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , , </i>;<br/>


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