<?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="E1:98"/><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>  )
 ;<br/>

<a NAME="E2:98"/><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="E3:98"/>
 <a href="jgraph_6.html#K5" target="_self">circle</a> 0,0,1 <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p5</font> where <font color="Olive">p5</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">p5</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="E4:98"/><b>then </b><i><font color="Green">E31</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/>
<b>thus </b><a NAME="E5:98"/>
( <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 implies <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">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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:98_1"/><i><font color="Green">E35</font></i>: 
<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><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:98_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">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 ) 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">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">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">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">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">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 ) )
 </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="98_1_1_1_1"><b>case </b></a><a NAME="E1:98_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">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"><b>hence </b><a NAME="E2:98_1_1_1_1"/>
<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">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/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1_2"><b>case </b></a><a NAME="E1:98_1_1_1_2"/>
(  <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">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="E2:98_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">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">p1</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:98_1_1_1_2"/>
<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">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>, <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="98_1_1_1_3"><b>case </b></a><a NAME="E1:98_1_1_1_3"/>
(  <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">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="E2:98_1_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">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">p2</font> <a href="jordan17.html#R1">are_in_this_order_on</a> <font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:98_1_1_1_3"/>
<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">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>, <a class="ref" href="jordan17.html#T11">JORDAN17:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1_4"><b>case </b></a><a NAME="E1:98_1_1_1_4"/>
(  <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">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="E2:98_1_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">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/><b>hence </b><a NAME="E3:98_1_1_1_4"/>
<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">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>, <a class="ref" href="jordan17.html#T10">JORDAN17:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:98_1"/>
<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">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>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:98"/>
( <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">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> implies <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 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:98_2"/><i><font color="Green">E36</font></i>: 
<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">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>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:98_2_1_1"/>
( (  <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> ) 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">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">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">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">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">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> ) )
 </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="98_2_1_1_1"><b>case </b></a><a NAME="E1:98_2_1_1_1"/>
(  <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/><div class="add"><b>hence </b><a NAME="E2:98_2_1_1_1"/>
<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
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_2_1_1_2"><b>case </b></a><a NAME="E1:98_2_1_1_2"/>
(  <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> &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> )
 ;<br/><div class="add"><a NAME="E2:98_2_1_1_2"/><b>then </b>
<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>, </i>;<br/><b>hence </b><a NAME="E3:98_2_1_1_2"/>
<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
 <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="98_2_1_1_3"><b>case </b></a><a NAME="E1:98_2_1_1_3"/>
(  <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">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> )
 ;<br/><div class="add"><a NAME="E2:98_2_1_1_3"/><b>then </b>
<font color="Maroon">p3</font>,<font color="Maroon">p4</font>,<font color="Maroon">p1</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
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:98_2_1_1_3"/>
<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
 <b>by </b><i>, <a class="ref" href="jordan17.html#T11">JORDAN17:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_2_1_1_4"><b>case </b></a><a NAME="E1:98_2_1_1_4"/>
(  <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">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> )
 ;<br/><div class="add"><a NAME="E2:98_2_1_1_4"/><b>then </b>
<font color="Maroon">p4</font>,<font color="Maroon">p1</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
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:98_2_1_1_4"/>
<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
 <b>by </b><i>, <a class="ref" href="jordan17.html#T10">JORDAN17:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:98_2"/>
<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><b>end;</b></div>


</div>
