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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></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">E6</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B 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">b<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">E7</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B 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">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">E8</font></i>: 
 <a href="jordan6.html#K5">Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">E9</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:8"/><i><font color="Green">E10</font></i>: 
 <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E6:8"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E5:8"><i><font color="Green">E10</font></i></a>, <a class="ref" href="jordan5c.html#D3">JORDAN5C:def 3</a></i>;<br/>
<a NAME="E7:8"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E5:8"><i><font color="Green">E10</font></i></a>, <a class="ref" href="jordan5c.html#D3">JORDAN5C:def 3</a></i>;<br/>
<a NAME="E8:8"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E1:8"><i><font color="Green">E6</font></i></a>, <a class="txt" href="jordan16.html#E5:8"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E9:8"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E4:8"><i><font color="Green">E9</font></i></a>, <a class="txt" href="jordan16.html#E6:8"><i><font color="Green">E11</font></i></a>, <a class="ref" href="jordan16.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E10:8"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K5">Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="jordan16.html#E3:8"><i><font color="Green">E8</font></i></a>, <a class="txt" href="jordan16.html#E8:8"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>

<a NAME="E11:8"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E2:8"><i><font color="Green">E7</font></i></a>, <a class="txt" href="jordan16.html#E5:8"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E12:8"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E4:8"><i><font color="Green">E9</font></i></a>, <a class="txt" href="jordan16.html#E7:8"><i><font color="Green">E12</font></i></a>, <a class="ref" href="jordan16.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E13:8"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K5">Segment</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="jordan16.html#E3:8"><i><font color="Green">E8</font></i></a>, <a class="txt" href="jordan16.html#E11:8"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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