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<b>let </b><font color="Maroon">A</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">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>;<br/><b>let </b><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/>









<a NAME="E1:8"/><i><font color="Green">E28</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q2</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> :  <a href="jordan5c.html#R1">LE</a> <font color="Olive">q</font>,<font color="Maroon">q2</font>,<font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="jordan6.html#D3">JORDAN6:def 3</a></i>;<br/>
<a NAME="E2:8"/><i><font color="Green">E29</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</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> :  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">q1</font>,<font color="Olive">q</font>,<font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="jordan6.html#D4">JORDAN6:def 4</a></i>;<br/>
<a NAME="E3:8"/><i><font color="Green">E49</font></i>: 
 <a href="jordan6.html#K5">Segment</a> <font color="Maroon">A</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> <span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan6.html#D5">JORDAN6:def 5</a></i>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E4:8"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">A</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>and </b><br/><a NAME="E5:8"/><i><font color="Green">E51</font></i>: 
 <a href="jordan5c.html#R1">LE</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font>,<font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 ;<br/>

<a NAME="E6:8"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="jordan5c.html#D3">JORDAN5C:def 3</a></i>;<br/>
<a NAME="E7:8"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="jordan5c.html#D3">JORDAN5C:def 3</a></i>;<br/>
<a NAME="E8:8"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:8"/>
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E10:8"/>
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K5">Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font>,<font color="Maroon">q2</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>

<a NAME="E11:8"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E12:8"/>
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q2</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E13:8"/>
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K5">Segment</a> <font color="Maroon">A</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">q1</font>,<font color="Maroon">q2</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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