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<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">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>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">y3</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>assume </b><a NAME="E1:95"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</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> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</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> &amp; <font color="Maroon">x3</font> <a href="hidden.html#R2">in</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> )
 ;<br/>

<b>consider </b><font color="Maroon">x1'</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="E3:95"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1'</font> &amp;  ex <font color="Olive">a11</font>, <font color="Olive">a12</font>, <font color="Olive">a13</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a11</font> <a href="real_1.html#K3">+</a> <font color="Olive">a12</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">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="Olive">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="Olive">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="Olive">a13</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="euclidlp.html#T29" target="_self">Th29</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="E5:95"/><i><font color="Green">E88</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><a class="ref" href="euclidlp.html#T30" target="_self">Th30</a></i>;<br/>
<b>consider </b><font color="Maroon">x2'</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="E7:95"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2'</font> &amp;  ex <font color="Olive">a21</font>, <font color="Olive">a22</font>, <font color="Olive">a23</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a21</font> <a href="real_1.html#K3">+</a> <font color="Olive">a22</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">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="Olive">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="Olive">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="Olive">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#T29" target="_self">Th29</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="E9:95"/><i><font color="Green">E90</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#T32" target="_self">Th32</a></i>;<br/>
<b>consider </b><font color="Maroon">x3'</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="E11:95"/><i><font color="Green">E105</font></i>: 
( <font color="Maroon">x3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x3'</font> &amp;  ex <font color="Olive">a31</font>, <font color="Olive">a32</font>, <font color="Olive">a33</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">a31</font> <a href="real_1.html#K3">+</a> <font color="Olive">a32</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">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="Olive">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="Olive">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="Olive">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#T29" target="_self">Th29</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="E13:95"/><i><font color="Green">E106</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="txt" href="euclidlp.html#E5:95"><i><font color="Green">E88</font></i></a></i>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E14:95"/>
<font color="Maroon">x</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>
 ;<br/>

<b>then 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="E16:95"/><i><font color="Green">E107</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> &amp;  ex <font color="Olive">b1</font>, <font color="Olive">b2</font>, <font color="Olive">b3</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">b1</font> <a href="real_1.html#K3">+</a> <font color="Olive">b2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">b3</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">b1</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"><font color="Olive">b2</font> <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="Olive">b3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> ) )
 ;<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="E18:95"/><i><font color="Green">E108</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">x</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">x1</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">x2</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">x3</font></span>)</span> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E9:95"><i><font color="Green">E90</font></i></a></i>;<br/>
<i><font color="Green">E109</font></i>: <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a11</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></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"><span class="p4">(<span class="default"><span class="p5">(<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="p5">(<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="p4">(<span class="default"><font color="Maroon">a23</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p3">(<span class="default"><span class="p4">(<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="p4">(<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="p3">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="euclidlp.html#T31" target="_self">Th31</a>, <a class="ref" href="euclidlp.html#T33" target="_self">Th33</a>, <a class="txt" href="euclidlp.html#E7:95"><i><font color="Green">E89</font></i></a>, <a class="ref" href="euclidlp.html#T35" target="_self">Th35</a></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"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a11</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a21</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a22</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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#K4">*</a> <font color="Maroon">a23</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p3">(<span class="default"><span class="p4">(<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="p4">(<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="p3">(<span class="default"><font color="Maroon">a33</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a11</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a12</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a13</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a21</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a22</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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#K4">*</a> <font color="Maroon">a23</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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#K4">*</a> <font color="Maroon">a31</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a32</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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#K4">*</a> <font color="Maroon">a33</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a11</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a21</font></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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a22</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a23</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a31</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a32</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y2</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#K4">*</a> <font color="Maroon">a33</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a11</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a21</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a31</font></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="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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a22</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a32</font></span>)</span></span>)</span> <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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a23</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a33</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">y3</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"><span class="p4">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a11</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a21</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a31</font></span>)</span></span>)</span> <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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a12</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a22</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a32</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">b1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a13</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a23</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a33</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<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></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<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></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<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></span>)</span></span>)</span>

<br/>.= 
1
<b>by </b><i><a class="ref" href="euclidlp.html#T35" target="_self">Th35</a>, <a class="ref" href="euclidlp.html#T31" target="_self">Th31</a>, <a class="ref" href="euclidlp.html#T33" target="_self">Th33</a>, <a class="txt" href="euclidlp.html#E7:95"><i><font color="Green">E89</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E21:95"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</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/>;<br/>


</div>
