<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">C</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">p</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">q</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><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E43</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font>
 ;<br/>

<a NAME="E3:22"/><i><font color="Green">E44</font></i>: 
 <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T16">SPRECT_1:16</a></i>;<br/>
<a NAME="E4:22"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<a NAME="E5:22"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<a NAME="E6:22"/><i><font color="Green">E54</font></i>: 
 <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="jordan6.html#T65">JORDAN6:65</a></i>;<br/>
<a NAME="E7:22"/><i><font color="Green">E55</font></i>: 
 <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="jordan6.html#T65">JORDAN6:65</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1"/>
( <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font> or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">q</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font> &amp; not  <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font> ) or ( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font> &amp;  <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> ) or ( <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font> &amp;  <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> ) or ( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font> &amp;  <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> ) or (  <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">p</font>,<font color="Maroon">C</font> &amp; not  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font> ) )
 </span><b>by </b><i>, , , <a class="ref" href="jordan16.html#T11">JORDAN16:11</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1"><b>suppose </b></a><a NAME="E1:22_1_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:22_1_1"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:22_1_2"/><i><font color="Green">E56</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">q</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green">E58</font></i>: 
not  <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:22_1_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><a NAME="E4:22_1_2"/><i><font color="Green">E60</font></i>: 
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:22_1_2"/>
not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E6:22_1_2"/><b>then </b>
 <a href="jordan5c.html#R1">LE</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/><b>hence </b><a NAME="E7:22_1_2"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , , <a class="ref" href="jordan16.html#T36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:22_1_3"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:22_1_3"/><i><font color="Green">E62</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:22_1_3"/><i><font color="Green">E63</font></i>: 
 <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E4:22_1_3"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><div><i><font color="Green">E66</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_3_1"/><i><font color="Green">E67</font></i>: 
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span>
 ;<br/><a NAME="E2:22_1_3_1"/><b>then </b>
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:22_1_3_1"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan6.html#T75">JORDAN6:75</a></i>;<br/><a NAME="E4:22_1_3_1"/>
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E5:22_1_3_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="jordan6.html#T74">JORDAN6:74</a></i>;<br/></div><b>end;</b></div><a NAME="E6:22_1_3"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan17.html#T3">JORDAN17:3</a></i>;<br/><a NAME="E7:22_1_3"/><b>then </b><i><font color="Green">E69</font></i>: 
 <a href="jordan5c.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan5c.html#T10">JORDAN5C:10</a></i>;<br/><a NAME="E8:22_1_3"/><i><font color="Green">E70</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E9:22_1_3"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>
 <b>by </b><i>, , <a class="ref" href="jordan16.html#T9">JORDAN16:9</a></i>;<br/><a NAME="E10:22_1_3"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan17.html#T4">JORDAN17:4</a></i>;<br/><a NAME="E11:22_1_3"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="jordan5c.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan5c.html#T10">JORDAN5C:10</a></i>;<br/><a NAME="E12:22_1_3"/><i><font color="Green">E73</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font>
 <b>by </b><i/>;<br/><a NAME="E13:22_1_3"/><b>then </b>
 <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font>
 <b>by </b><i>, , <a class="ref" href="jordan16.html#T9">JORDAN16:9</a></i>;<br/><a NAME="E14:22_1_3"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E15:22_1_3"/><i><font color="Green">E75</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="jordan6.html#T21">JORDAN6:21</a></i>;<br/><a NAME="E16:22_1_3"/><i><font color="Green">E76</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="jordan6.html#T20">JORDAN6:20</a></i>;<br/><a NAME="E17:22_1_3"/>
<span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="jordan6.html#D9">JORDAN6:def 9</a></i>;<br/><a NAME="E18:22_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E19:22_1_3"/><b>then </b><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="topreal8.html#T1">TOPREAL8:1</a></i>;<br/><a NAME="E20:22_1_3"/><i><font color="Green">E78</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>by </b><i>, , , , <a class="ref" href="jordan16.html#T36">JORDAN16:36</a></i>;<br/><a NAME="E21:22_1_3"/><i><font color="Green">E79</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font> <a href="topreal1.html#R1">is_an_arc_of</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , , , <a class="ref" href="jordan16.html#T36">JORDAN16:36</a></i>;<br/><a NAME="E22:22_1_3"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E23:22_1_3"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , <a class="ref" href="jordan_a.html#T1" target="_self">Th1</a>, <a class="ref" href="topreal1.html#T5">TOPREAL1:5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:22_1_4"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:22_1_4"/><i><font color="Green">E121</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:22_1_4"/><i><font color="Green">E122</font></i>: 
 <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font>
 ;<br/><div class="add"><a NAME="E4:22_1_4"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan17.html#T3">JORDAN17:3</a></i>;<br/><a NAME="E5:22_1_4"/><b>then </b><i><font color="Green">E123</font></i>: 
 <a href="jordan5c.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan5c.html#T10">JORDAN5C:10</a></i>;<br/><a NAME="E6:22_1_4"/><i><font color="Green">E124</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E7:22_1_4"/><b>then </b><i><font color="Green">E125</font></i>: 
 <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>
 <b>by </b><i>, , <a class="ref" href="jordan16.html#T9">JORDAN16:9</a></i>;<br/><a NAME="E8:22_1_4"/><i><font color="Green">E126</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T22">JORDAN6:22</a></i>;<br/> <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> = 
<span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
;<br/><b>hence </b><a NAME="E10:22_1_4"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , , , , <a class="ref" href="jordan16.html#T36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_5"><b>suppose </b></a><b>that </b><a NAME="E1:22_1_5"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:22_1_5"/><i><font color="Green">E128</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:22_1_5"/><i><font color="Green">E129</font></i>: 
 <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font>
 ;<br/><div class="add"><a NAME="E4:22_1_5"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan17.html#T4">JORDAN17:4</a></i>;<br/><a NAME="E5:22_1_5"/><b>then </b><i><font color="Green">E130</font></i>: 
 <a href="jordan5c.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">q</font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan5c.html#T10">JORDAN5C:10</a></i>;<br/><a NAME="E6:22_1_5"/><i><font color="Green">E131</font></i>: 
 <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font>
 <b>by </b><i/>;<br/><a NAME="E7:22_1_5"/><b>then </b><i><font color="Green">E132</font></i>: 
 <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font>
 <b>by </b><i>, , <a class="ref" href="jordan16.html#T9">JORDAN16:9</a></i>;<br/><a NAME="E8:22_1_5"/><i><font color="Green">E133</font></i>: 
 <a href="jordan6.html#K4">R_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T26">JORDAN6:26</a></i>;<br/> <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> = 
<span class="p1">(<span class="default"><a href="jordan6.html#K4">R_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K3">L_Segment</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="jordan6.html#K3">L_Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">q</font>
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
;<br/><b>hence </b><a NAME="E10:22_1_5"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , , , , <a class="ref" href="jordan16.html#T36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6"><b>suppose </b></a><b>that </b><a NAME="E1:22_1_6"/><i><font color="Green">E134</font></i>: 
 <a href="jordan6.html#R1">LE</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">p</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:22_1_6"/><i><font color="Green">E135</font></i>: 
not  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>,<font color="Maroon">C</font>
 ;<br/><div class="add"><a NAME="E3:22_1_6"/><i><font color="Green">E136</font></i>: 
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K5">Segment</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E4:22_1_6"/>
not <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:22_1_6"/><b>then </b>
 <a href="jordan5c.html#R1">LE</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">C</font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/><b>hence </b><a NAME="E6:22_1_6"/>
 <a href="jordan7.html#K1">Segment</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">C</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , , <a class="ref" href="jordan16.html#T36">JORDAN16:36</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
