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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font>, <font color="Olive" title="b3">y2</font>, <font color="Olive" title="b4">y3</font>, <font color="Olive" title="b5">x2</font>, <font color="Olive" title="b6">x3</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b2">y1</font>,<font color="Olive" title="b3">y2</font>,<font color="Olive" title="b4">y3</font>) &amp; <font color="Olive" title="b5">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b2">y1</font>,<font color="Olive" title="b3">y2</font>,<font color="Olive" title="b4">y3</font>) &amp; <font color="Olive" title="b6">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b2">y1</font>,<font color="Olive" title="b3">y2</font>,<font color="Olive" title="b4">y3</font>) holds <br/> <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b1">x1</font>,<font color="Olive" title="b5">x2</font>,<font color="Olive" title="b6">x3</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b2">y1</font>,<font color="Olive" title="b3">y2</font>,<font color="Olive" title="b4">y3</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">y1</font>, <font color="Maroon" title="c4">y2</font>, <font color="Maroon" title="c5">y3</font>, <font color="Maroon" title="c6">x2</font>, <font color="Maroon" title="c7">x3</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>) &amp; <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>) &amp; <font color="Maroon" title="c7">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>) implies  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c7">x3</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>) )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:94"/><span class="lab"><font color="Green" title="E76">A1</font></span>: 
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>)
 <span class="kw">and </span><br/><a NAME="E2:94"/><span class="lab"><font color="Green" title="E77">A2</font></span>: 
<font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>)
 <span class="kw">and </span><br/><a NAME="E3:94"/><span class="lab"><font color="Green" title="E78">A3</font></span>: 
<font color="Maroon" title="c7">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c7">x3</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>)</span><br/>

<a NAME="E4:94"/>
 ex <font color="Olive" title="b1">x29</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x29</font> &amp;  ex <font color="Olive" title="b2">a21</font>, <font color="Olive" title="b3">a22</font>, <font color="Olive" title="b4">a23</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">a21</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">a22</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b4">a23</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b1">x29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a21</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a22</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a23</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:94"><span class="lab"><font color="Green" title="E77">A2</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">a21</font>, <font color="Maroon" title="c9">a22</font>, <font color="Maroon" title="c10">a23</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E6:94"/><span class="lab"><font color="Green" title="E79">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">a21</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c9">a22</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c10">a23</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E7:94"/><span class="lab"><font color="Green" title="E80">A5</font></span>: 
<font color="Maroon" title="c6">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a21</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">a22</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">a23</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span>
 ;<br/>
<a NAME="E8:94"/>
 ex <font color="Olive" title="b1">x19</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x19</font> &amp;  ex <font color="Olive" title="b2">a11</font>, <font color="Olive" title="b3">a12</font>, <font color="Olive" title="b4">a13</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">a11</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">a12</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b4">a13</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b1">x19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a11</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a12</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a13</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:94"><span class="lab"><font color="Green" title="E76">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">a11</font>, <font color="Maroon" title="c12">a12</font>, <font color="Maroon" title="c13">a13</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E10:94"/><span class="lab"><font color="Green" title="E81">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">a11</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c13">a13</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E11:94"/><span class="lab"><font color="Green" title="E82">A7</font></span>: 
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a11</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a12</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a13</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span>
 ;<br/>
<span class="kw">let </span><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c7">x3</font>) or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E12:94"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c7">x3</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>)</span><br/>

<a NAME="E13:94"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x9</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x9</font> &amp;  ex <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">b2</font>, <font color="Olive" title="b4">b3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b4">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b1">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">b1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x3</font></span>)</span> ) )
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">b1</font>, <font color="Maroon" title="c16">b2</font>, <font color="Maroon" title="c17">b3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E15:94"/><span class="lab"><font color="Green" title="E83">A8</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c16">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c17">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E16:94"/><span class="lab"><font color="Green" title="E84">A9</font></span>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c7">x3</font></span>)</span>
 ;<br/>
<a NAME="E17:94"/>
 ex <font color="Olive" title="b1">x39</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Maroon" title="c7">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x39</font> &amp;  ex <font color="Olive" title="b2">a31</font>, <font color="Olive" title="b3">a32</font>, <font color="Olive" title="b4">a33</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">a31</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">a32</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b4">a33</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b1">x39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a31</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a32</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a33</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:94"><span class="lab"><font color="Green" title="E78">A3</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c18">a31</font>, <font color="Maroon" title="c19">a32</font>, <font color="Maroon" title="c20">a33</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E19:94"/><span class="lab"><font color="Green" title="E85">A10</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">a31</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c19">a32</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c20">a33</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E20:94"/><span class="lab"><font color="Green" title="E86">A11</font></span>: 
<font color="Maroon" title="c7">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">a31</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">a32</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">a33</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span>
 ;<br/>
<span class="lab"><font color="Green" title="E87">A12</font></span>: <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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a11</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">a21</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a31</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">a22</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c19">a32</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">a13</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">a23</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c20">a33</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">a11</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c13">a13</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">a21</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c9">a22</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c10">a23</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">a31</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c19">a32</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c20">a33</font></span>)</span></span>)</span>

<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:94"><span class="lab"><font color="Green" title="E81">A6</font></span></a>, <a class="txt" href="#E6:94"><span class="lab"><font color="Green" title="E79">A4</font></span></a>, <a class="txt" href="#E19:94"><span class="lab"><font color="Green" title="E85">A10</font></span></a>, <a class="txt" href="#E15:94"><span class="lab"><font color="Green" title="E83">A8</font></span></a></span>
;<br/>
<font color="Maroon" title="c14">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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a11</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">a13</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">a21</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">a22</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">a23</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">a31</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c19">a32</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c20">a33</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:94"><span class="lab"><font color="Green" title="E82">A7</font></span></a>, <a class="txt" href="#E7:94"><span class="lab"><font color="Green" title="E80">A5</font></span></a>, <a class="txt" href="#E20:94"><span class="lab"><font color="Green" title="E86">A11</font></span></a>, <a class="txt" href="#E16:94"><span class="lab"><font color="Green" title="E84">A9</font></span></a>, <a class="ref" href="euclidlp.html#T22" target="_self" title="EUCLIDLP:th.22">Th27</a></span>
<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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a11</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">a13</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</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" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">a21</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">a22</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">a23</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">a31</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c19">a32</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c20">a33</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#T22" target="_self" title="EUCLIDLP:th.22">Th27</a></span>
<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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a11</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">a13</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</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" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">a21</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">a22</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">a23</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</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" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a31</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c19">a32</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c20">a33</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#T22" target="_self" title="EUCLIDLP:th.22">Th27</a></span>
<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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a11</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">a21</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">a22</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">a13</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">a23</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</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" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a31</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c19">a32</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c20">a33</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#T24" target="_self" title="EUCLIDLP:th.24">Th29</a></span>
<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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a11</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">a21</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a31</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a12</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">a22</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c19">a32</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">y2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</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" title="c15">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">a13</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">a23</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">b3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c20">a33</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">y3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#T24" target="_self" title="EUCLIDLP:th.24">Th29</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E23:94"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c5">y3</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:94"><span class="lab"><font color="Green" title="E87">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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