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

<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font>, <font color="Maroon" title="c3">p3</font>, <font color="Maroon" title="c4">p4</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">P</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E61">A1</font></i>: 
( <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span>}</span>  &amp; <font color="Maroon" title="c4">p4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c5">P</font> )
 ;<br/>

<a NAME="E2:67"/><b>then </b><i><font color="Green" title="E62">A2</font></i>: 
<font color="Maroon" title="c5">P</font> <a href="topreal2.html#NR1" title="TOPREAL2:NR.1">is_simple_closed_curve</a> 
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T36" title="JGRAPH_3:th.36">JGRAPH_3:36</a></i>;<br/>
<a NAME="E3:67"/><b>then </b><i><font color="Green" title="E63">A3</font></i>: 
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="ref" href="jordan6.html#D8" title="JORDAN6:def.8">JORDAN6:def 8</a></i>;<br/>
<a NAME="E4:67"/><i><font color="Green" title="E64">A4</font></i>: 
( <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span>}</span>  &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Maroon" title="c2">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Maroon" title="c3">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Maroon" title="c4">p4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Maroon" title="c4">p4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c5">P</font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E2:67"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="jordan7.html#T5" title="JORDAN7:th.5">JORDAN7:5</a></i>;<br/>
<a NAME="E5:67"/><i><font color="Green" title="E65">A5</font></i>: 
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">p7</font> where <font color="Olive" title="b1">p7</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive" title="b1">p7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Olive" title="b1">p7</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="jgraph_5.html#T37" target="_self" title="JGRAPH_5:th.37">Th37</a></i>;<br/>
<a NAME="E6:67"/>
 <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="jgraph_5.html#T32" target="_self" title="JGRAPH_5:th.32">Th32</a></i>;<br/>
<a NAME="E7:67"/><b>then </b><i><font color="Green" title="E66">A6</font></i>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<a NAME="E8:67"/><b>then </b><i><font color="Green" title="E67">A7</font></i>: 
<font color="Maroon" title="c4">p4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E4:67"><i><font color="Green" title="E64">A4</font></i></a>, <a class="txt" href="jgraph_5.html#E5:67"><i><font color="Green" title="E65">A5</font></i></a></i>;<br/>
<a NAME="E9:67"/><b>then </b><i><font color="Green" title="E68">A8</font></i>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="jgraph_5.html#T47" target="_self" title="JGRAPH_5:th.47">Th47</a></i>;<br/>
<a NAME="E10:67"/><b>then </b>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c3">p3</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E3:67"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/>
<a NAME="E11:67"/><b>then </b>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:67"><i><font color="Green" title="E67">A7</font></i></a>, <a class="txt" href="jgraph_5.html#E9:67"><i><font color="Green" title="E68">A8</font></i></a>, <a class="ref" href="jordan6.html#D10" title="JORDAN6:def.10">JORDAN6:def 10</a></i>;<br/>
<a NAME="E12:67"/><b>then </b><i><font color="Green" title="E69">A9</font></i>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p4</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E2:67"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="jordan6.html#T72" title="JORDAN6:th.72">JORDAN6:72</a></i>;<br/>
<a NAME="E13:67"/><i><font color="Green" title="E70">A10</font></i>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E9:67"><i><font color="Green" title="E68">A8</font></i></a>, <a class="ref" href="jgraph_5.html#T47" target="_self" title="JGRAPH_5:th.47">Th47</a></i>;<br/>
<a NAME="E14:67"/><b>then </b>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c2">p2</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E3:67"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/>
<a NAME="E15:67"/><b>then </b><i><font color="Green" title="E71">A11</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:67"><i><font color="Green" title="E67">A7</font></i></a>, <a class="txt" href="jgraph_5.html#E13:67"><i><font color="Green" title="E70">A10</font></i></a>, <a class="ref" href="jordan6.html#D10" title="JORDAN6:def.10">JORDAN6:def 10</a></i>;<br/>
<a NAME="E16:67"/>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E2:67"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="jordan6.html#T73" title="JORDAN6:th.73">JORDAN6:73</a></i>;<br/>
<a NAME="E17:67"/><b>then </b><i><font color="Green" title="E72">A12</font></i>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p4</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E2:67"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="jgraph_5.html#E15:67"><i><font color="Green" title="E71">A11</font></i></a>, <a class="ref" href="jordan6.html#T72" title="JORDAN6:th.72">JORDAN6:72</a></i>;<br/>
<a NAME="E18:67"/><i><font color="Green" title="E73">A13</font></i>: 
<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E13:67"><i><font color="Green" title="E70">A10</font></i></a>, <a class="ref" href="jgraph_5.html#T47" target="_self" title="JGRAPH_5:th.47">Th47</a></i>;<br/>
<a NAME="E19:67"/><b>then </b>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c1">p1</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E3:67"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="jordan5c.html#T10" title="JORDAN5C:th.10">JORDAN5C:10</a></i>;<br/>
<a NAME="E20:67"/><b>then </b>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:67"><i><font color="Green" title="E67">A7</font></i></a>, <a class="txt" href="jgraph_5.html#E18:67"><i><font color="Green" title="E73">A13</font></i></a>, <a class="ref" href="jordan6.html#D10" title="JORDAN6:def.10">JORDAN6:def 10</a></i>;<br/>
<a NAME="E21:67"/><b>then </b>
<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p4</font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E2:67"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="jgraph_5.html#E17:67"><i><font color="Green" title="E72">A12</font></i></a>, <a class="ref" href="jordan6.html#T72" title="JORDAN6:th.72">JORDAN6:72</a></i>;<br/>
<b>hence </b><a NAME="E22:67"/>
 ex <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font>, <font color="Olive" title="b4">q3</font>, <font color="Olive" title="b5">q4</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>( <font color="Olive" title="b1">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a>  &amp; ( for <font color="Olive" title="b6">q</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> holds  <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">q</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b6">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> ) &amp; <font color="Olive" title="b2">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">p1</font> &amp; <font color="Olive" title="b3">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p2</font> &amp; <font color="Olive" title="b4">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Olive" title="b5">q4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">p4</font> &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b3">q2</font>,<font color="Olive" title="b4">q3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b4">q3</font>,<font color="Olive" title="b5">q4</font>,<font color="Maroon" title="c5">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:67"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="jgraph_5.html#E7:67"><i><font color="Green" title="E66">A6</font></i></a>, <a class="txt" href="jgraph_5.html#E12:67"><i><font color="Green" title="E69">A9</font></i></a>, <a class="txt" href="jgraph_5.html#E17:67"><i><font color="Green" title="E72">A12</font></i></a>, <a class="ref" href="jgraph_5.html#T62" target="_self" title="JGRAPH_5:th.62">Th62</a></i>;<br/>


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