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

<b>let </b><font color="Maroon">p1</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">p2</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">p3</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">p4</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">P</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>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>set </b><font color="Maroon">K</font> =  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1;<br/>
<b>assume </b><a NAME="E1:97"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="jgraph_6.html#K5" target="_self">circle</a> 0,0,1 &amp; <font color="Maroon">f</font> <a href="funct_2.html#R2">=</a>  <a href="jgraph_3.html#K1">Sq_Circ</a>  &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> )
 ;<br/>

<a NAME="E2:97"/><i><font color="Green">E30</font></i>: 
 <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="topreal2.html#NR1" target="_self">is_simple_closed_curve</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:97"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> 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">p</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 </span>}</span> 
 
<b>by </b><i>, <a class="txt" href="jgraph_6.html#E10"><i><font color="Green">Lemma40</font></i></a></i>;<br/>
<a NAME="E4:97"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">P</font> <a href="topreal2.html#NR1" target="_self">is_simple_closed_curve</a> 
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T36">JGRAPH_3:36</a></i>;<br/>
<a NAME="E5:97"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font>
 
<b>by </b><i>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/>
<a NAME="E6:97"/><i><font color="Green">E37</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font>
 
<b>by </b><i>, , <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/>
<a NAME="E7:97"/>
 <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> 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">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) or ( <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) or ( <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) or ( <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="jgraph_6.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E8:97"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 
<b>by </b><i>, , , <a class="ref" href="jgraph_3.html#T33">JGRAPH_3:33</a></i>;<br/>
<a NAME="E9:97"/><i><font color="Green">E76</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</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>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E10:97"/>
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> 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">p</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 </span>}</span> 
 
<b>by </b><i>, <a class="txt" href="jgraph_6.html#E10"><i><font color="Green">Lemma40</font></i></a></i>;<br/>
<a NAME="E11:97"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">P</font> <a href="topreal2.html#NR1" target="_self">is_simple_closed_curve</a> 
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T36">JGRAPH_3:36</a></i>;<br/>
<a NAME="E12:97"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 
<b>by </b><i>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E14:97"/><i><font color="Green">E78</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E15:97"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E16:97"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 
<b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E18:97"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E19:97"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i>, , <a class="txt" href="jgraph_6.html#E26:97"><i><font color="Green">E99</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E20:97"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 
<b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">x3</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E22:97"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">x3</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x3</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x3</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E23:97"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">p3</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E24:97"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 
<b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">x4</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E26:97"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">x4</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x4</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x4</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E27:97"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">p4</font> <a href="hidden.html#R2">in</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:97_1"/><i><font color="Green">E101</font></i>: 
not <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">p3</font>,<font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div><i><font color="Green">E102</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:97_1_1"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">p4</font>,<font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_1_1_1"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) )
 </span><b>by </b><i>, <a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1"><b>case </b></a><a NAME="E1:97_1_1_1_1_1"/><i><font color="Green">E122</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_1_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_1_1_1_1"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_1_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E18:97"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_1_1_1_1"/><b>then </b><i><font color="Green">E124</font></i>: 
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p4</font> or <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_1_1_1_1"/>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E7:97_1_1_1_1_1"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p4</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_2"><b>case </b></a><a NAME="E1:97_1_1_1_1_2"/><i><font color="Green">E125</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_1_1_1_2"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_1_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_1_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_1_1_1_2"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p4</font> or <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_1_1_1_2"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> &amp; <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_3"><b>case </b></a><a NAME="E1:97_1_1_1_1_3"/><i><font color="Green">E158</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_1_1_1_3"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_1_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_1_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_1_1_1_3"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p4</font> or <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_1_1_1_3"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> &amp; <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_1_1_1_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_4"><b>case </b></a><a NAME="E1:97_1_1_1_1_4"/><i><font color="Green">E159</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_1_1_1_4"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_1_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_1_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_1_1_1_4"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p4</font> or <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_1_1_1_4"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> &amp; <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_1_1_1_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:97_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div><div><i><font color="Green">E162</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:97_1_2"/><i><font color="Green">E163</font></i>: 
<font color="Maroon">p1</font>,<font color="Maroon">p3</font>,<font color="Maroon">p4</font>,<font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_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="E1:97_1_2_1_1"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) )
 </span><b>by </b><i>, <a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_2_1_1_1"><b>case </b></a><a NAME="E1:97_1_2_1_1_1"/>
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_2_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_2_1_1_1"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_2_1_1_1"/><b>then </b><i><font color="Green">E164</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E7:97_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E8:97_1_2_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_2_1_1_2"><b>case </b></a><a NAME="E1:97_1_2_1_1_2"/>
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_2_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_2_1_1_2"/><b>then </b><i><font color="Green">E165</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_2_1_1_2"/><b>then </b><i><font color="Green">E166</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_2_1_1_2"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E7:97_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> or <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E9:97_1_2_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_2_1_1_3"><b>case </b></a><a NAME="E1:97_1_2_1_1_3"/>
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_2_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_2_1_1_3"/><b>then </b><i><font color="Green">E167</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_2_1_1_3"/><b>then </b><i><font color="Green">E169</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_2_1_1_3"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E7:97_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> or <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E9:97_1_2_1_1_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_2_1_1_4"><b>case </b></a><a NAME="E1:97_1_2_1_1_4"/><i><font color="Green">E171</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_2_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_2_1_1_4"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_2_1_1_4"/><b>then </b><i><font color="Green">E172</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_2_1_1_4"/><b>then </b>
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E7:97_1_2_1_1_4"/><b>then </b>
<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font>
 <b>by </b><i>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_2_1_1_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:97_1_2"/>
contradiction
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_3_1"/>
( <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">p4</font>,<font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 or <font color="Maroon">p1</font>,<font color="Maroon">p3</font>,<font color="Maroon">p2</font>,<font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 or <font color="Maroon">p1</font>,<font color="Maroon">p3</font>,<font color="Maroon">p4</font>,<font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 or <font color="Maroon">p1</font>,<font color="Maroon">p4</font>,<font color="Maroon">p2</font>,<font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 or <font color="Maroon">p1</font>,<font color="Maroon">p4</font>,<font color="Maroon">p3</font>,<font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 </span><b>by </b><i>, <a class="txt" href="jgraph_6.html#E23:97"><i><font color="Green">E98</font></i></a>, <a class="txt" href="jgraph_6.html#E27:97"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_6.html#E2:97_1"><i><font color="Green">E102</font></i></a>, <a class="ref" href="jgraph_6.html#T18" target="_self">Th18</a>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, <a class="ref" href="jordan17.html#T27">JORDAN17:27</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_1"><b>case </b></a><a NAME="E1:97_1_3_1_1"/>
<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">p4</font>,<font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:97_1_3_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_2"><b>case </b></a><a NAME="E1:97_1_3_1_2"/><i><font color="Green">E173</font></i>: 
<font color="Maroon">p1</font>,<font color="Maroon">p3</font>,<font color="Maroon">p2</font>,<font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_3_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_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="E1:97_1_3_1_2_1_1"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) )
 </span><b>by </b><i>, <a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_2_1_1_1"><b>case </b></a><a NAME="E1:97_1_3_1_2_1_1_1"/><i><font color="Green">E175</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_2_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_2_1_1_1"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_3_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_2_1_1_2"><b>case </b></a><a NAME="E1:97_1_3_1_2_1_1_2"/><i><font color="Green">E177</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_2_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_2_1_1_2"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_3_1_2_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_2_1_1_3"><b>case </b></a><a NAME="E1:97_1_3_1_2_1_1_3"/><i><font color="Green">E179</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_2_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_2_1_1_3"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_3_1_2_1_1_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_2_1_1_4"><b>case </b></a><a NAME="E1:97_1_3_1_2_1_1_4"/><i><font color="Green">E180</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_2_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_2_1_1_4"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E8:97_1_3_1_2_1_1_4"/>
contradiction
 <b>by </b><i><a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:97_1_3_1_2"/>
contradiction
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_3"><b>case </b></a><a NAME="E1:97_1_3_1_3"/>
<font color="Maroon">p1</font>,<font color="Maroon">p3</font>,<font color="Maroon">p4</font>,<font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:97_1_3_1_3"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_4"><b>case </b></a><a NAME="E1:97_1_3_1_4"/><i><font color="Green">E181</font></i>: 
<font color="Maroon">p1</font>,<font color="Maroon">p4</font>,<font color="Maroon">p2</font>,<font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_3_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_3_1_4_1_1"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) )
 </span><b>by </b><i>, <a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_4_1_1_1"><b>case </b></a><a NAME="E1:97_1_3_1_4_1_1_1"/><i><font color="Green">E182</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_4_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_4_1_1_1"/><b>then </b><i><font color="Green">E184</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_4_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_4_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_4_1_1_1"/><b>then </b><i><font color="Green">E206</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_4_1_1_1"/><b>then </b><i><font color="Green">E207</font></i>: 
<font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_3_1_4_1_1_1"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E18:97"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E9:97_1_3_1_4_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E10:97_1_3_1_4_1_1_1"/><b>then </b><i><font color="Green">E208</font></i>: 
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> or <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E11:97_1_3_1_4_1_1_1"/><b>then </b>
<font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><b>hence </b><a NAME="E12:97_1_3_1_4_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_4_1_1_2"><b>case </b></a><a NAME="E1:97_1_3_1_4_1_1_2"/><i><font color="Green">E209</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_4_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_4_1_1_2"/><b>then </b><i><font color="Green">E210</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_4_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_4_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_4_1_1_2"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_4_1_1_2"/><b>then </b><i><font color="Green">E211</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or ( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> ) )
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_3_1_4_1_1_2"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E18:97"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E9:97_1_3_1_4_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E10:97_1_3_1_4_1_1_2"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> or <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E11:97_1_3_1_4_1_1_2"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_4_1_1_3"><b>case </b></a><a NAME="E1:97_1_3_1_4_1_1_3"/><i><font color="Green">E212</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_4_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_4_1_1_3"/><b>then </b><i><font color="Green">E213</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_4_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_4_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_4_1_1_3"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_4_1_1_3"/><b>then </b><i><font color="Green">E214</font></i>: 
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or ( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> ) )
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_3_1_4_1_1_3"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E18:97"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E9:97_1_3_1_4_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E10:97_1_3_1_4_1_1_3"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> or <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E11:97_1_3_1_4_1_1_3"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_4_1_1_4"><b>case </b></a><a NAME="E1:97_1_3_1_4_1_1_4"/><i><font color="Green">E215</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_4_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_4_1_1_4"/><b>then </b><i><font color="Green">E216</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_4_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E19:97"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E5:97_1_3_1_4_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E6:97_1_3_1_4_1_1_4"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E7:97_1_3_1_4_1_1_4"/><b>then </b><i><font color="Green">E217</font></i>: 
<font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_3_1_4_1_1_4"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="txt" href="jgraph_6.html#E18:97"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a>, <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E9:97_1_3_1_4_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E10:97_1_3_1_4_1_1_4"/><b>then </b>
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> or <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E11:97_1_3_1_4_1_1_4"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:97_1_3_1_4"/>
contradiction
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_5"><b>case </b></a><a NAME="E1:97_1_3_1_5"/><i><font color="Green">E218</font></i>: 
<font color="Maroon">p1</font>,<font color="Maroon">p4</font>,<font color="Maroon">p3</font>,<font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_3_1_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_3_1_5_1_1"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 ) )
 </span><b>by </b><i>, <a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_5_1_1_1"><b>case </b></a><a NAME="E1:97_1_3_1_5_1_1_1"/><i><font color="Green">E219</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_5_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_5_1_1_1"/><b>then </b><i><font color="Green">E220</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_5_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_3_1_5_1_1_1"/><b>then </b><i><font color="Green">E221</font></i>: 
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_3_1_5_1_1_1"/>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E7:97_1_3_1_5_1_1_1"/><b>then </b><i><font color="Green">E222</font></i>: 
<font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_3_1_5_1_1_1"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E9:97_1_3_1_5_1_1_1"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E10:97_1_3_1_5_1_1_1"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> or <font color="Maroon">p2</font>,<font color="Maroon">p3</font>,<font color="Maroon">p4</font>,<font color="Maroon">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 <b>by </b><i>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/><b>hence </b><a NAME="E11:97_1_3_1_5_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jgraph_6.html#T20" target="_self">Th20</a>, , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_5_1_1_2"><b>case </b></a><a NAME="E1:97_1_3_1_5_1_1_2"/>
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_5_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_5_1_1_2"/><b>then </b><i><font color="Green">E223</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_5_1_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_3_1_5_1_1_2"/><b>then </b><i><font color="Green">E224</font></i>: 
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_3_1_5_1_1_2"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E7:97_1_3_1_5_1_1_2"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E8:97_1_3_1_5_1_1_2"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_5_1_1_3"><b>case </b></a><a NAME="E1:97_1_3_1_5_1_1_3"/>
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p3</font>,<font color="Maroon">p2</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_5_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_5_1_1_3"/><b>then </b>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_5_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_3_1_5_1_1_3"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E6:97_1_3_1_5_1_1_3"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_3_1_5_1_1_4"><b>case </b></a><a NAME="E1:97_1_3_1_5_1_1_4"/><i><font color="Green">E225</font></i>: 
(  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p4</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">p4</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 )
 ;<br/><div class="add"><a NAME="E2:97_1_3_1_5_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:97_1_3_1_5_1_1_4"/><b>then </b><i><font color="Green">E226</font></i>: 
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font>,<font color="Maroon">P</font> ) )
 <b>by </b><i><a class="ref" href="jordan17.html#D1">JORDAN17:def 1</a></i>;<br/><a NAME="E4:97_1_3_1_5_1_1_4"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E5:97_1_3_1_5_1_1_4"/><b>then </b><i><font color="Green">E227</font></i>: 
( <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E6:97_1_3_1_5_1_1_4"/>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">p1</font>,<font color="Maroon">p3</font>, <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 <b>by </b><i>, , <a class="ref" href="jordan6.html#T73">JORDAN6:73</a></i>;<br/><a NAME="E7:97_1_3_1_5_1_1_4"/><b>then </b><i><font color="Green">E228</font></i>: 
<font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, , , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E8:97_1_3_1_5_1_1_4"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> or <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, <a class="txt" href="jgraph_6.html#E22:97"><i><font color="Green">E96</font></i></a>, , <a class="ref" href="jordan6.html#T72">JORDAN6:72</a></i>;<br/><a NAME="E9:97_1_3_1_5_1_1_4"/><b>then </b>
( <font color="Maroon">p4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> or <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p3</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E10:97_1_3_1_5_1_1_4"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="jordan17.html#T12">JORDAN17:12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:97_1_3_1_5"/>
contradiction
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:97_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E29:97"/>
<font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">p3</font>,<font color="Maroon">p4</font> <a href="jordan17.html#R1">are_in_this_order_on</a>  <a href="jgraph_6.html#NK1" target="_self">rectangle</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1
 ;<br/>


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