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<b>let </b><font color="Maroon" title="c1">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">p2</font>, <font color="Maroon" title="c4">q1</font>, <font color="Maroon" title="c5">q2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c1">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> &amp; <font color="Maroon" title="c4">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> &amp; <font color="Maroon" title="c5">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> )
 ;<br/>

<a NAME="E2:34"/><i><font color="Green" title="E23">A2</font></i>: 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c5">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">q2</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E1:34"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="jordan6.html#T31" target="_self" title="JORDAN6:th.31">Th31</a></i>;<br/>
<a NAME="E3:34"/>
<font color="Maroon" title="c1">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E1:34"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="jordan5b.html#T14" title="JORDAN5B:th.14">JORDAN5B:14</a></i>;<br/>
<a NAME="E4:34"/><b>then </b>
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c4">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c4">q1</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E1:34"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="jordan6.html#T31" target="_self" title="JORDAN6:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E5:34"/>
 <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c5">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E2:34"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/>


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