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

<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">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">x3</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">P</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="euclidlp.html#K5" target="_self">plane_of_REAL</a> <font color="Maroon">n</font>;<br/>









<b>assume </b><a NAME="E1:105"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font>,<font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font> <a href="euclidlp.html#R3" target="_self">are_lindependent2</a>  )
 ;<br/>

<a NAME="E2:105"/>
<font color="Maroon">P</font> <a href="hidden.html#R2">in</a>  <a href="euclidlp.html#K5" target="_self">plane_of_REAL</a> <font color="Maroon">n</font>
 
;<br/>
<b>then consider </b><font color="Maroon">P'</font> being   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font></span>)</span><b> such that </b><br/><a NAME="E4:105"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P'</font> &amp;  ex <font color="Olive">y1</font>, <font color="Olive">y2</font>, <font color="Olive">y3</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> st <font color="Maroon">P'</font> <a href="hidden.html#R1">=</a>  <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Olive">y1</font>,<font color="Olive">y2</font>,<font color="Olive">y3</font> )
 ;<br/>
<b>consider </b><font color="Maroon">y1</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">y2</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">y3</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E6:105"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font>,<font color="Maroon">y3</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E7:105"><i><font color="Green">E89</font></i></a></i>;<br/>
<a NAME="E7:105"/><i><font color="Green">E89</font></i>: 
 <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E6:105"><i><font color="Green">E88</font></i></a>, <a class="txt" href="euclidlp.html#E9:105"><i><font color="Green">E90</font></i></a>, <a class="ref" href="euclidlp.html#T28" target="_self">Th28</a></i>;<br/>
<b>consider </b><font color="Maroon">x'</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E9:105"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> &amp;  ex <font color="Olive">a1'</font>, <font color="Olive">a2'</font>, <font color="Olive">a3'</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a1'</font> <a href="real_1.html#K3">+</a> <font color="Olive">a2'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">a3'</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">a1'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Olive">a2'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Olive">a3'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="euclidlp.html#E6:105"><i><font color="Green">E88</font></i></a>, <a class="txt" href="euclidlp.html#E9:105"><i><font color="Green">E90</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">a11</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a12</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a13</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E11:105"/><i><font color="Green">E105</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">a11</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a13</font> <a href="hidden.html#R1">=</a> 1 &amp; <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">a11</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">x'</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E13:105"/><i><font color="Green">E106</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> &amp;  ex <font color="Olive">a1'</font>, <font color="Olive">a2'</font>, <font color="Olive">a3'</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a1'</font> <a href="real_1.html#K3">+</a> <font color="Olive">a2'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">a3'</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">a1'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Olive">a2'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Olive">a3'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="euclidlp.html#E6:105"><i><font color="Green">E88</font></i></a>, <a class="txt" href="euclidlp.html#E9:105"><i><font color="Green">E90</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">a21</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a22</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a23</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E15:105"/><i><font color="Green">E107</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">a21</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a22</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a23</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a21</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a22</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> )
 <b>by </b><i><a class="ref" href="euclidlp.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon">x'</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E17:105"/><i><font color="Green">E108</font></i>: 
( <font color="Maroon">x3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> &amp;  ex <font color="Olive">a1'</font>, <font color="Olive">a2'</font>, <font color="Olive">a3'</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a1'</font> <a href="real_1.html#K3">+</a> <font color="Olive">a2'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">a3'</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">a1'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Olive">a2'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Olive">a3'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="euclidlp.html#E6:105"><i><font color="Green">E88</font></i></a>, <a class="txt" href="euclidlp.html#E9:105"><i><font color="Green">E90</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">a31</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a32</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a33</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E19:105"/><i><font color="Green">E109</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">a31</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a32</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a33</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a31</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T38" target="_self">Th38</a></i>;<br/>
<a NAME="E20:105"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclidlp.html#T36" target="_self">Th36</a>, </i>;<br/>
<a NAME="E21:105"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">x3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclidlp.html#D2" target="_self">Def2</a>, </i>;<br/>
<i><font color="Green">E112</font></i>: <font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E43"><i><font color="Green">Lemma98</font></i></a>, <a class="ref" href="euclidlp.html#T37" target="_self">Th37</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></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"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</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"><span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a22</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">a23</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</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">a22</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">a23</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<i><font color="Green">E113</font></i>: <font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T36" target="_self">Th36</a>, , <a class="ref" href="euclidlp.html#T40" target="_self">Th40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></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"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</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"><span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a32</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">a33</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</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">a32</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">a33</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>
<b>consider </b><font color="Maroon">c1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">c2</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">d1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">d2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E25:105"/><i><font color="Green">E114</font></i>: 
( <font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c2</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> &amp; <font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">d1</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E6:105"><i><font color="Green">E88</font></i></a>, <a class="ref" href="euclidlp.html#T41" target="_self">Th41</a>, , </i>;<br/>
<a NAME="E26:105"/><i><font color="Green">E151</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E43"><i><font color="Green">Lemma98</font></i></a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:105_3"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/><b>consider </b><font color="Maroon">x'</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E3:105_3"/><i><font color="Green">E153</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> &amp;  ex <font color="Olive">a1'</font>, <font color="Olive">a2'</font>, <font color="Olive">a3'</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a1'</font> <a href="real_1.html#K3">+</a> <font color="Olive">a2'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">a3'</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">a1'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Olive">a2'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Olive">a3'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="euclidlp.html#E9:105"><i><font color="Green">E90</font></i></a>, </i>;<br/><b>consider </b><font color="Maroon">b1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b2</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b3</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:105_3"/><i><font color="Green">E154</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">b3</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E11:105"><i><font color="Green">E105</font></i></a></i>;<br/><font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon">y1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E13:105"><i><font color="Green">E106</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></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">x1</font> <a href="euclid.html#K8">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</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">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p0">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</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">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p0">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</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">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p0">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></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> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</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">x1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p0">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a12</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></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> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a13</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">b3</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">y2</font> <a href="euclid.html#K8">-</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"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">y3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">y1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c1</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c2</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d1</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">d2</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c1</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c2</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></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">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d1</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d2</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c2</font> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></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">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d1</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d2</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d1</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d2</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">d2</font> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></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"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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">x1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></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"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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">x1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></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"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></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"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></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"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T7">EUCLID_4:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T7">EUCLID_4:7</a></i>
;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E8:105_3"/><i><font color="Green">E155</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <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"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</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"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">d2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E9:105_3"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>
 <b>by </b><i><a class="txt" href="euclidlp.html#E15:105"><i><font color="Green">E107</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E28:105"/><b>then </b>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E29:105"/>
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>
 <b>by </b><i><a class="ref" href="euclidlp.html#T35" target="_self">Th35</a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
