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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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><b>that </b><br/><a NAME="E1:21"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font>
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green" title="E19">A2</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font>
 ;<br/>

<a NAME="E3:21"/><i><font color="Green" title="E20">A3</font></i>: 
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T16" title="SPRECT_1:th.16">SPRECT_1:16</a></i>;<br/>
<a NAME="E4:21"/><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="jordan_a.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="jordan7.html#T5" title="JORDAN7:th.5">JORDAN7:5</a></i>;<br/>
<a NAME="E5:21"/><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="jordan_a.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="jordan7.html#T5" title="JORDAN7:th.5">JORDAN7:5</a></i>;<br/>
<a NAME="E6:21"/><i><font color="Green" title="E23">A6</font></i>: 
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="jordan6.html#T65" title="JORDAN6:th.65">JORDAN6:65</a></i>;<br/>
<a NAME="E7:21"/><i><font color="Green" title="E24">A7</font></i>: 
 <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="jordan6.html#T65" title="JORDAN6:th.65">JORDAN6:65</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1"/>
( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font> or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">q</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font> &amp; not  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font> ) or ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> ) or ( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> ) or ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">C</font> &amp; not  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font> ) )
 </span><b>by </b><i><a class="txt" href="jordan_a.html#E3:21"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="jordan_a.html#E4:21"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="jordan_a.html#E5:21"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="jordan16.html#T11" title="JORDAN16:th.11">JORDAN16:11</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1"><b>suppose </b></a><a NAME="E1:21_1_1"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_1"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E4:21"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="jordan_a.html#T17" target="_self" title="JORDAN_A:th.17">Th17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:21_1_2"/><i><font color="Green" title="E25">A8</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">q</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E2:21_1_2"/><i><font color="Green" title="E26">A9</font></i>: 
not  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E3:21_1_2"/><i><font color="Green" title="E27">A10</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 ;<br/><div class="add"><a NAME="E4:21_1_2"/><i><font color="Green" title="E28">A11</font></i>: 
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_2"><i><font color="Green" title="E25">A8</font></i></a>, <a class="ref" href="jordan_a.html#T9" target="_self" title="JORDAN_A:th.9">Th9</a></i>;<br/><a NAME="E5:21_1_2"/>
not <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_2"><i><font color="Green" title="E26">A9</font></i></a>, <a class="txt" href="jordan_a.html#E3:21_1_2"><i><font color="Green" title="E27">A10</font></i></a>, <a class="ref" href="jordan_a.html#T6" target="_self" title="JORDAN_A:th.6">Th6</a></i>;<br/><a NAME="E6:21_1_2"/><b>then </b>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="jordan6.html#D10" title="JORDAN6:def.10">JORDAN6:def 10</a></i>;<br/><b>hence </b><a NAME="E7:21_1_2"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="jordan_a.html#E4:21_1_2"><i><font color="Green" title="E28">A11</font></i></a>, <a class="ref" href="jordan16.html#T36" title="JORDAN16:th.36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:21_1_3"/><i><font color="Green" title="E25">A12</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E2:21_1_3"/><i><font color="Green" title="E26">A13</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E3:21_1_3"/><i><font color="Green" title="E27">A14</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E4:21_1_3"/><i><font color="Green" title="E28">A15</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 ;<br/><div class="add"><div><i><font color="Green" title="E29">A16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_3_1"/><i><font color="Green" title="E30">A17</font></i>: 
 <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font></span>)</span>
 ;<br/><a NAME="E2:21_1_3_1"/><b>then </b>
 <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:21_1_3_1"/><b>then </b><i><font color="Green" title="E31">A18</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="jordan6.html#T75" title="JORDAN6:th.75">JORDAN6:75</a></i>;<br/><a NAME="E4:21_1_3_1"/>
 <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21_1_3_1"><i><font color="Green" title="E30">A17</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E5:21_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E3:21_1_3_1"><i><font color="Green" title="E31">A18</font></i></a>, <a class="ref" href="jordan6.html#T74" title="JORDAN6:th.74">JORDAN6:74</a></i>;<br/></div><b>end;</b></div><a NAME="E6:21_1_3"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_3"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="jordan17.html#T3" title="JORDAN17:th.3">JORDAN17:3</a></i>;<br/><a NAME="E7:21_1_3"/><b>then </b><i><font color="Green" title="E30">A19</font></i>: 
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/><a NAME="E8:21_1_3"/><i><font color="Green" title="E31">A20</font></i>: 
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan_a.html#T15" target="_self" title="JORDAN_A:th.15">Th15</a></i>;<br/><a NAME="E9:21_1_3"/><b>then </b><i><font color="Green" title="E32">A21</font></i>: 
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="jordan_a.html#E7:21_1_3"><i><font color="Green" title="E30">A19</font></i></a>, <a class="ref" href="jordan16.html#T9" title="JORDAN16:th.9">JORDAN16:9</a></i>;<br/><a NAME="E10:21_1_3"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E3:21_1_3"><i><font color="Green" title="E27">A14</font></i></a>, <a class="ref" href="jordan17.html#T4" title="JORDAN17:th.4">JORDAN17:4</a></i>;<br/><a NAME="E11:21_1_3"/><b>then </b><i><font color="Green" title="E33">A22</font></i>: 
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>, <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/><a NAME="E12:21_1_3"/><i><font color="Green" title="E34">A23</font></i>: 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="ref" href="jordan_a.html#T16" target="_self" title="JORDAN_A:th.16">Th16</a></i>;<br/><a NAME="E13:21_1_3"/><b>then </b>
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E11:21_1_3"><i><font color="Green" title="E33">A22</font></i></a>, <a class="ref" href="jordan16.html#T9" title="JORDAN16:th.9">JORDAN16:9</a></i>;<br/><a NAME="E14:21_1_3"/><b>then </b><i><font color="Green" title="E35">A24</font></i>: 
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan_a.html#E9:21_1_3"><i><font color="Green" title="E32">A21</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E15:21_1_3"/><i><font color="Green" title="E36">A25</font></i>: 
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="ref" href="jordan6.html#T21" title="JORDAN6:th.21">JORDAN6:21</a></i>;<br/><a NAME="E16:21_1_3"/><i><font color="Green" title="E37">A26</font></i>: 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="ref" href="jordan6.html#T20" title="JORDAN6:th.20">JORDAN6:20</a></i>;<br/><a NAME="E17:21_1_3"/>
<span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 <b>by </b><i><a class="ref" href="jordan6.html#D9" title="JORDAN6:def.9">JORDAN6:def 9</a></i>;<br/><a NAME="E18:21_1_3"/><b>then </b><i><font color="Green" title="E38">A27</font></i>: 
<span class="p1">(<span class="default"><a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="jordan_a.html#E5:21_1_3"><i><font color="Green" title="E29">A16</font></i></a>, <a class="txt" href="jordan_a.html#E14:21_1_3"><i><font color="Green" title="E35">A24</font></i></a>, <a class="txt" href="jordan_a.html#E15:21_1_3"><i><font color="Green" title="E36">A25</font></i></a>, <a class="txt" href="jordan_a.html#E16:21_1_3"><i><font color="Green" title="E37">A26</font></i></a>, <a class="ref" href="topreal8.html#T1" title="TOPREAL8:th.1">TOPREAL8:1</a>, <a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/><a NAME="E19:21_1_3"/><i><font color="Green" title="E39">A28</font></i>: 
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_3"><i><font color="Green" title="E25">A12</font></i></a>, <a class="txt" href="jordan_a.html#E7:21_1_3"><i><font color="Green" title="E30">A19</font></i></a>, <a class="txt" href="jordan_a.html#E8:21_1_3"><i><font color="Green" title="E31">A20</font></i></a>, <a class="ref" href="jordan16.html#T36" title="JORDAN16:th.36">JORDAN16:36</a></i>;<br/><a NAME="E20:21_1_3"/><i><font color="Green" title="E40">A29</font></i>: 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E4:21_1_3"><i><font color="Green" title="E28">A15</font></i></a>, <a class="txt" href="jordan_a.html#E11:21_1_3"><i><font color="Green" title="E33">A22</font></i></a>, <a class="txt" href="jordan_a.html#E12:21_1_3"><i><font color="Green" title="E34">A23</font></i></a>, <a class="ref" href="jordan16.html#T36" title="JORDAN16:th.36">JORDAN16:36</a></i>;<br/><a NAME="E21:21_1_3"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_3"><i><font color="Green" title="E26">A13</font></i></a>, <a class="txt" href="jordan_a.html#E3:21_1_3"><i><font color="Green" title="E27">A14</font></i></a>, <a class="ref" href="jordan_a.html#T13" target="_self" title="JORDAN_A:th.13">Th13</a></i>;<br/><b>hence </b><a NAME="E22:21_1_3"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E18:21_1_3"><i><font color="Green" title="E38">A27</font></i></a>, <a class="txt" href="jordan_a.html#E19:21_1_3"><i><font color="Green" title="E39">A28</font></i></a>, <a class="txt" href="jordan_a.html#E20:21_1_3"><i><font color="Green" title="E40">A29</font></i></a>, <a class="ref" href="topreal1.html#T5" title="TOPREAL1:th.5">TOPREAL1:5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:21_1_4"/><i><font color="Green" title="E25">A30</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E2:21_1_4"/><i><font color="Green" title="E26">A31</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E3:21_1_4"/><i><font color="Green" title="E27">A32</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font>
 ;<br/><div class="add"><a NAME="E4:21_1_4"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_4"><i><font color="Green" title="E26">A31</font></i></a>, <a class="ref" href="jordan17.html#T3" title="JORDAN17:th.3">JORDAN17:3</a></i>;<br/><a NAME="E5:21_1_4"/><b>then </b><i><font color="Green" title="E28">A33</font></i>: 
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/><a NAME="E6:21_1_4"/><i><font color="Green" title="E29">A34</font></i>: 
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan_a.html#T15" target="_self" title="JORDAN_A:th.15">Th15</a></i>;<br/><a NAME="E7:21_1_4"/><b>then </b><i><font color="Green" title="E30">A35</font></i>: 
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="jordan_a.html#E5:21_1_4"><i><font color="Green" title="E28">A33</font></i></a>, <a class="ref" href="jordan16.html#T9" title="JORDAN16:th.9">JORDAN16:9</a></i>;<br/><a NAME="E8:21_1_4"/><i><font color="Green" title="E31">A36</font></i>: 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_4"><i><font color="Green" title="E25">A30</font></i></a>, <a class="ref" href="jordan6.html#T22" title="JORDAN6:th.22">JORDAN6:22</a></i>;<br/> <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> = 
<span class="p1">(<span class="default"><a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_4"><i><font color="Green" title="E26">A31</font></i></a>, <a class="txt" href="jordan_a.html#E3:21_1_4"><i><font color="Green" title="E27">A32</font></i></a>, <a class="ref" href="jordan_a.html#T13" target="_self" title="JORDAN_A:th.13">Th13</a></i>
<br/>.= 
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>
<b>by </b><i><a class="txt" href="jordan_a.html#E7:21_1_4"><i><font color="Green" title="E30">A35</font></i></a>, <a class="txt" href="jordan_a.html#E8:21_1_4"><i><font color="Green" title="E31">A36</font></i></a>, <a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
;<br/><b>hence </b><a NAME="E10:21_1_4"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_4"><i><font color="Green" title="E25">A30</font></i></a>, <a class="txt" href="jordan_a.html#E5:21_1_4"><i><font color="Green" title="E28">A33</font></i></a>, <a class="txt" href="jordan_a.html#E6:21_1_4"><i><font color="Green" title="E29">A34</font></i></a>, <a class="ref" href="jordan16.html#T36" title="JORDAN16:th.36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_5"><b>suppose </b></a><b>that </b><a NAME="E1:21_1_5"/><i><font color="Green" title="E25">A37</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E2:21_1_5"/><i><font color="Green" title="E26">A38</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E3:21_1_5"/><i><font color="Green" title="E27">A39</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font>
 ;<br/><div class="add"><a NAME="E4:21_1_5"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E3:21_1_5"><i><font color="Green" title="E27">A39</font></i></a>, <a class="ref" href="jordan17.html#T4" title="JORDAN17:th.4">JORDAN17:4</a></i>;<br/><a NAME="E5:21_1_5"/><b>then </b><i><font color="Green" title="E28">A40</font></i>: 
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">q</font>, <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/><a NAME="E6:21_1_5"/><i><font color="Green" title="E29">A41</font></i>: 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="ref" href="jordan_a.html#T16" target="_self" title="JORDAN_A:th.16">Th16</a></i>;<br/><a NAME="E7:21_1_5"/><b>then </b><i><font color="Green" title="E30">A42</font></i>: 
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E5:21_1_5"><i><font color="Green" title="E28">A40</font></i></a>, <a class="ref" href="jordan16.html#T9" title="JORDAN16:th.9">JORDAN16:9</a></i>;<br/><a NAME="E8:21_1_5"/><i><font color="Green" title="E31">A43</font></i>: 
 <a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="jordan_a.html#E6:21"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_5"><i><font color="Green" title="E25">A37</font></i></a>, <a class="ref" href="jordan6.html#T26" title="JORDAN6:th.26">JORDAN6:26</a></i>;<br/> <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> = 
<span class="p1">(<span class="default"><a href="jordan6.html#K4" title="JORDAN6:func.4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_5"><i><font color="Green" title="E26">A38</font></i></a>, <a class="txt" href="jordan_a.html#E3:21_1_5"><i><font color="Green" title="E27">A39</font></i></a>, <a class="ref" href="jordan_a.html#T13" target="_self" title="JORDAN_A:th.13">Th13</a></i>
<br/>.= 
 <a href="jordan6.html#K3" title="JORDAN6:func.3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="txt" href="jordan_a.html#E7:21_1_5"><i><font color="Green" title="E30">A42</font></i></a>, <a class="txt" href="jordan_a.html#E8:21_1_5"><i><font color="Green" title="E31">A43</font></i></a>, <a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
;<br/><b>hence </b><a NAME="E10:21_1_5"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_5"><i><font color="Green" title="E25">A37</font></i></a>, <a class="txt" href="jordan_a.html#E5:21_1_5"><i><font color="Green" title="E28">A40</font></i></a>, <a class="txt" href="jordan_a.html#E6:21_1_5"><i><font color="Green" title="E29">A41</font></i></a>, <a class="ref" href="jordan16.html#T36" title="JORDAN16:th.36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_6"><b>suppose </b></a><b>that </b><a NAME="E1:21_1_6"/><i><font color="Green" title="E25">A44</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">C</font>
 <b>and </b><br/><a NAME="E2:21_1_6"/><i><font color="Green" title="E26">A45</font></i>: 
not  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font>
 ;<br/><div class="add"><a NAME="E3:21_1_6"/><i><font color="Green" title="E27">A46</font></i>: 
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan6.html#K5" title="JORDAN6:func.5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="jordan_a.html#E1:21_1_6"><i><font color="Green" title="E25">A44</font></i></a>, <a class="ref" href="jordan_a.html#T12" target="_self" title="JORDAN_A:th.12">Th12</a></i>;<br/><a NAME="E4:21_1_6"/>
not <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21_1_6"><i><font color="Green" title="E26">A45</font></i></a>, <a class="ref" href="jordan_a.html#T7" target="_self" title="JORDAN_A:th.7">Th7</a></i>;<br/><a NAME="E5:21_1_6"/><b>then </b>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>, <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <font color="Maroon" title="c1">C</font>, <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="jordan6.html#D10" title="JORDAN6:def.10">JORDAN6:def 10</a></i>;<br/><b>hence </b><a NAME="E6:21_1_6"/>
 <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">C</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="jordan_a.html#E7:21"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="jordan_a.html#E3:21_1_6"><i><font color="Green" title="E27">A46</font></i></a>, <a class="ref" href="jordan16.html#T36" title="JORDAN16:th.36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
