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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>assume </b><a NAME="E1:62"/><i><font color="Green">E59</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 </span>}</span>  &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:62"/><b>then </b><i><font color="Green">E60</font></i>: 
 <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="jgraph_5.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E3:62"/><i><font color="Green">E61</font></i>: 
 <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0 ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_5.html#T38" target="_self">Th38</a></i>;<br/>
<a NAME="E4:62"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="topreal2.html#NR1" target="_self">is_simple_closed_curve</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_3.html#T36">JGRAPH_3:36</a></i>;<br/>
<a NAME="E5:62"/>
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_5.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E6:62"/><b>then </b><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E7:62"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="jgraph_4.html#T120">JGRAPH_4:120</a></i>;<br/>
<a NAME="E8:62"/>
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
;<br/>
<a NAME="E9:62"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E10:62"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
;<br/>
<a NAME="E11:62"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:62"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a>  is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_4.html#T140">JGRAPH_4:140</a></i>;<br/>
<a NAME="E13:62"/><i><font color="Green">E68</font></i>: 
 <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_5.html#T36" target="_self">Th36</a></i>;<br/>
<a NAME="E14:62"/><i><font color="Green">E69</font></i>: 
 <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_5.html#T36" target="_self">Th36</a></i>;<br/>
<div><i><font color="Green">E70</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> )
 </span><b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_1_1_1"><b>case </b></a><a NAME="E1:62_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:62_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E13:62"><i><font color="Green">E68</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_1_1_2"><b>case </b></a><a NAME="E1:62_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:62_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E14:62"><i><font color="Green">E69</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E71</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:62_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E7:62"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E9:62"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E11:62"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E12:62"><i><font color="Green">E67</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E3:62_2"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E4:62"><i><font color="Green">E62</font></i></a>, <a class="txt" href="jgraph_5.html#E15:62"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jordan7.html#T3">JORDAN7:3</a></i>;<br/><a NAME="E4:62_2"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E4:62"><i><font color="Green">E62</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:62_2"/>
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E4:62"><i><font color="Green">E62</font></i></a>, <a class="ref" href="jordan7.html#T1">JORDAN7:1</a></i>;<br/><a NAME="E6:62_2"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E4:62"><i><font color="Green">E62</font></i></a>, <a class="txt" href="jgraph_5.html#E14:62"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="jgraph_5.html#E4:62_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="jordan6.html#T71">JORDAN6:71</a></i>;<br/><b>hence </b><a NAME="E7:62_2"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_3"/>
( ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_1"><b>suppose </b></a><a NAME="E1:62_3_1"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <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><b> such that </b><br/><a NAME="E3:62_3_1"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E2:62"><i><font color="Green">E60</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <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><b> such that </b><br/><a NAME="E5:62_3_1"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:62"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_1"><i><font color="Green">E72</font></i></a></i>;<br/><a NAME="E6:62_3_1"/><i><font color="Green">E75</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_4.html#T135">JGRAPH_4:135</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <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><b> such that </b><br/><a NAME="E8:62_3_1"/><i><font color="Green">E76</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_1"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E9:62_3_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E6:62_3_1"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E8:62_3_1"><i><font color="Green">E76</font></i></a></i>;<br/><a NAME="E10:62_3_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="jgraph_5.html#T60" target="_self">Th60</a></i>;<br/><b>hence </b><a NAME="E11:62_3_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E3:62"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E16:62"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_1"><i><font color="Green">E72</font></i></a>, <a class="txt" href="jgraph_5.html#E3:62_3_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="jgraph_5.html#E9:62_3_1"><i><font color="Green">E77</font></i></a>, <a class="ref" href="jgraph_4.html#T120">JGRAPH_4:120</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_2"><b>suppose </b></a><a NAME="E1:62_3_2"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <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><b> such that </b><br/><a NAME="E3:62_3_2"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E2:62"><i><font color="Green">E60</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <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><b> such that </b><br/><a NAME="E5:62_3_2"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E2:62"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_2"><i><font color="Green">E72</font></i></a></i>;<br/><a NAME="E6:62_3_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:62_3_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="jgraph_4.html#T120">JGRAPH_4:120</a></i>;<br/><b>hence </b><a NAME="E7:62_3_2"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="jgraph_4.html#T120">JGRAPH_4:120</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3"><b>suppose </b></a><a NAME="E1:62_3_3"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><a NAME="E2:62_3_3"/><i><font color="Green">E73</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_4.html#T135">JGRAPH_4:135</a></i>;<br/><a NAME="E3:62_3_3"/><i><font color="Green">E74</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jgraph_4.html#T135">JGRAPH_4:135</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <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><b> such that </b><br/><a NAME="E5:62_3_3"/><i><font color="Green">E75</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:62"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3"><i><font color="Green">E72</font></i></a></i>;<br/><a NAME="E6:62_3_3"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_3"><i><font color="Green">E75</font></i></a>, <a class="ref" href="jgraph_5.html#T60" target="_self">Th60</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <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><b> such that </b><br/><a NAME="E8:62_3_3"/><i><font color="Green">E77</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:62"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3"><i><font color="Green">E72</font></i></a></i>;<br/><a NAME="E9:62_3_3"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E8:62_3_3"><i><font color="Green">E77</font></i></a>, <a class="ref" href="jgraph_5.html#T60" target="_self">Th60</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <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><b> such that </b><br/><a NAME="E11:62_3_3"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_3"><i><font color="Green">E75</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <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><b> such that </b><br/><a NAME="E13:62_3_3"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>10</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E8:62_3_3"><i><font color="Green">E77</font></i></a></i>;<br/><a NAME="E14:62_3_3"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E2:62_3_3"><i><font color="Green">E73</font></i></a>, <a class="txt" href="jgraph_5.html#E11:62_3_3"><i><font color="Green">E79</font></i></a></i>;<br/><a NAME="E15:62_3_3"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E3:62_3_3"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E13:62_3_3"><i><font color="Green">E80</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_3_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_3_3_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3_1_1_1"><b>case </b></a><a NAME="E1:62_3_3_1_1_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><a NAME="E2:62_3_3_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="jgraph_4.html#K9">-FanMorphS</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E6:62"><i><font color="Green">E63</font></i></a>, <a class="ref" href="jgraph_4.html#T120">JGRAPH_4:120</a></i>;<br/><a NAME="E3:62_3_3_1_1_1"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E4:62"><i><font color="Green">E62</font></i></a>, <a class="txt" href="jgraph_5.html#E15:62_3_3"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3_1_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="jordan7.html#T3">JORDAN7:3</a></i>;<br/><b>hence </b><a NAME="E4:62_3_3_1_1_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3_1_1_2"><b>case </b></a><a NAME="E1:62_3_3_1_1_2"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_3_3_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_3_3_1_1_2_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  )
 </span><b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_3"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E8:62_3_3"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3_1_1_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="jgraph_5.html#T51" target="_self">Th51</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:62_3_3_1_1_2_1_1_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> 
 ;<br/><div class="add"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> = 
1 <a href="square_1.html#K5">^2</a> 
<b>by </b><i><a class="txt" href="jgraph_5.html#E11:62_3_3"><i><font color="Green">E79</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_5.html#E13:62_3_3"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3_1_1_2_1_1_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>
;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> 

;<br/><a NAME="E4:62_3_3_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="square_1.html#T109">SQUARE_1:109</a></i>;<br/><a NAME="E5:62_3_3_1_1_2_1_1_1"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/><a NAME="E6:62_3_3_1_1_2_1_1_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_3_3_1_1_2_1_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_3_3_1_1_2_1_1_1_3"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>
 ;<br/><a NAME="E2:62_3_3_1_1_2_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_5.html#E5:62_3_3"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E8:62_3_3"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><b>hence </b><a NAME="E3:62_3_3_1_1_2_1_1_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62_3_3_1_1_2_1_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jgraph_5.html#E6:62_3_3_1_1_2_1_1_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3_1_1_2_1_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/></div><b>end;</b></div><a NAME="E8:62_3_3_1_1_2_1_1_1"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E4:62"><i><font color="Green">E62</font></i></a>, <a class="txt" href="jgraph_5.html#E15:62_3_3"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3_1_1_2_1_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jgraph_5.html#E4:62_3_3_1_1_2_1_1_1"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_3_1_1_2_1_1_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_5.html#E6:62_3_3_1_1_2_1_1_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="jordan6.html#T71">JORDAN6:71</a></i>;<br/><b>hence </b><a NAME="E9:62_3_3_1_1_2_1_1_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_3_3_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:62_3_3_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> 
 ;<br/><div class="add"><a NAME="E2:62_3_3_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E11:62_3_3"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_5.html#E13:62_3_3"><i><font color="Green">E80</font></i></a></i>;<br/><a NAME="E3:62_3_3_1_1_2_1_1_2"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E7:62"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E9:62"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E11:62"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E12:62"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_5.html#E1:62_3_3"><i><font color="Green">E72</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E4:62_3_3_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E5:62_3_3"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E8:62_3_3"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_5.html#E11:62_3_3"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_5.html#E13:62_3_3"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jgraph_5.html#E2:62_3_3_1_1_2_1_1_2"><i><font color="Green">E84</font></i></a>, <a class="ref" href="jgraph_5.html#T30" target="_self">Th30</a></i>;<br/><a NAME="E5:62_3_3_1_1_2_1_1_2"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:62"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jgraph_5.html#E2:62_3_3"><i><font color="Green">E73</font></i></a>, <a class="txt" href="jgraph_5.html#E3:62_3_3"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E6:62_3_3"><i><font color="Green">E76</font></i></a>, <a class="txt" href="jgraph_5.html#E9:62_3_3"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_5.html#E11:62_3_3"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_5.html#E13:62_3_3"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jgraph_5.html#E14:62_3_3"><i><font color="Green">E81</font></i></a>, <a class="txt" href="jgraph_5.html#E15:62_3_3"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_5.html#E3:62_3_3_1_1_2_1_1_2"><i><font color="Green">E85</font></i></a>, <a class="ref" href="jgraph_5.html#T59" target="_self">Th59</a></i>;<br/><b>hence </b><a NAME="E6:62_3_3_1_1_2_1_1_2"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:62_3_3_1_1_2"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E17:62_3_3"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="jordan5c.html#R1">LE</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>6</sub></font>, <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>6</sub></font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan6.html#D10">JORDAN6:def 10</a><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
