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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>, <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>, <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>, <font color="Maroon">q2</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="E1:34"/><i><font color="Green">E37</font></i>: 
( <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> &amp; <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 ;<br/>

<a NAME="E2:34"/><i><font color="Green">E47</font></i>: 
 <a href="jordan6.html#K3" target="_self">L_Segment</a> <font color="Maroon">P</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K4" target="_self">R_Segment</a> <font color="Maroon">P</font>,<font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">q2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:34"/>
<font color="Maroon">P</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>
 
<b>by </b><i>, <a class="ref" href="jordan5b.html#T14">JORDAN5B:14</a></i>;<br/>
<a NAME="E4:34"/><b>then </b>
 <a href="jordan6.html#K4" target="_self">R_Segment</a> <font color="Maroon">P</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K3" target="_self">L_Segment</a> <font color="Maroon">P</font>,<font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">q1</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:34"/>
 <a href="jordan6.html#K5" target="_self">Segment</a> <font color="Maroon">P</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font>,<font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5" target="_self">Segment</a> <font color="Maroon">P</font>,<font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">q2</font>,<font color="Maroon">q1</font>
 <b>by </b><i/>;<br/>


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