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<b>let </b><font color="Maroon">a1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a3</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">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">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">x</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>assume </b><a NAME="E1:99"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">x1</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>  &amp; <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> &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">a1</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">a2</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">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> &amp; not <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> 1 )
 ;<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="E3:99"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">x</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">x1</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">x2</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">x3</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">a1'</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a2'</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a3'</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:99"/><i><font color="Green">E88</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">a1'</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a2'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">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="Maroon">a1'</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">a2'</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">a3'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T31" target="_self">Th31</a></i>;<br/>
<i><font color="Green">E89</font></i>:  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a2'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a3'</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T30" target="_self">Th30</a>, <a class="ref" href="euclidlp.html#T32" target="_self">Th32</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E7:99"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a3</font></span>)</span> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="ref" href="euclidlp.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E8:99"/><b>then </b><i><font color="Green">E90</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="euclidlp.html#T30" target="_self">Th30</a></i>;<br/>
<b>set </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span>;<br/>
<i><font color="Green">E105</font></i>:  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T2">EUCLID_4:2</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">1 <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</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">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i>, <a class="ref" href="euclidlp.html#T33" target="_self">Th33</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"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</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">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</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"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></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">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</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"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></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"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a1'</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a2'</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a3'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T64">XCMPLX_1:64</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="euclidlp.html#E5:99"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/>
<b>hence </b><a NAME="E11:99"/>
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</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#E6:99"><i><font color="Green">E89</font></i></a></i>;<br/>


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