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

<b>let </b><font color="Maroon">a1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">y2</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">y1</font>, <font color="Maroon">y1</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>



















<b>assume </b><a NAME="E1:42"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="euclidlp.html#R3" target="_self">are_lindependent2</a> 
 ;<br/>

<b>assume </b><a NAME="E2:42"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span> )
 ;<br/>

<i><font color="Green">E88</font></i>: <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<a NAME="E4:42"/><i><font color="Green">E89</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:42_2"/><i><font color="Green">E90</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<i><font color="Green">E105</font></i>: <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
0 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
;<br/>
<a NAME="E3:42_2"/><b>then </b><i><font color="Green">E106</font></i>: 
( <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="real_1.html#K1">-</a> <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:42_2"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<i><font color="Green">E108</font></i>: <font color="Maroon">y1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a>, , </i>
<br/>.= 
<font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<i><font color="Green">E109</font></i>: <font color="Maroon">y2</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default">0 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4">EUCLID_4:4</a>, <a class="ref" href="euclidlp.html#T1" target="_self">Th1</a>, <a class="ref" href="euclidlp.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4">EUCLID_4:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T7">EUCLID_4:7</a></i>
<br/>.= 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
;<br/>
<a NAME="E8:42_2"/><b>then </b><i><font color="Green">E110</font></i>: 
( <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="real_1.html#K1">-</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:42_2"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="euclidlp.html#T3" target="_self">Th3</a></i>;<br/>
<font color="Maroon">y1</font> = 
<span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default">0 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a>, , , <a class="ref" href="euclidlp.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<b>hence </b><a NAME="E11:42_2"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<i><font color="Green">E112</font></i>: <font color="Maroon">x1</font> = 
1 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4">EUCLID_4:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4">EUCLID_4:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>
;<br/>
<i><font color="Green">E113</font></i>: <span class="p1">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<i><font color="Green">E114</font></i>: <font color="Maroon">x2</font> = 
1 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4">EUCLID_4:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T6">EUCLID_4:6</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span>
<b>by </b><i/>
;<br/>
<b>set </b><font color="Maroon">c1</font> = <font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c2</font> = <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">d1</font> = <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">d2</font> = <font color="Maroon">a1</font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>;<br/>
<b>take </b>
<font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
;<br/>

<b>take </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
;<br/>

<b>take </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
;<br/>

<b>take </b>
<font color="Maroon">a1</font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
;<br/>

<b>thus </b><a NAME="E8:42"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span> )
 <b>by </b><i>, </i>;<br/>


</div>
