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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">x2</font>, <font color="Olive" title="b5">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="b2">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="Olive" title="b3">x1</font>,<font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">x3</font> &amp;  ex <font color="Olive" title="b6">c1</font>, <font color="Olive" title="b7">c2</font>, <font color="Olive" title="b8">c3</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="b6">c1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b7">c2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b8">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">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="Olive" title="b6">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b3">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b7">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b4">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="b8">c3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b5">x3</font></span>)</span> ) holds <br/> <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</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="b3">x1</font>,<font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">x3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">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">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="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font>,<font color="Olive" title="b4">x3</font> &amp;  ex <font color="Olive" title="b5">c1</font>, <font color="Olive" title="b6">c2</font>, <font color="Olive" title="b7">c3</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="b5">c1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b6">c2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b7">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">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="Olive" title="b5">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b2">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b6">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b3">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="b7">c3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b4">x3</font></span>)</span> ) holds <br/> <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</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">x1</font>,<font color="Olive" title="b3">x2</font>,<font color="Olive" title="b4">x3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font> &amp;  ex <font color="Olive" title="b1">c1</font>, <font color="Olive" title="b2">c2</font>, <font color="Olive" title="b3">c3</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="b1">c1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b2">c2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">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="Olive" title="b1">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">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="b3">c3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span> ) implies  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</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="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:100"/><span class="lab"><font color="Green" title="E76">A1</font></span>: 
<font color="Maroon" title="c3">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="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font>
 <span class="kw">and </span><br/><a NAME="E2:100"/><span class="lab"><font color="Green" title="E77">A2</font></span>: 
 ex <font color="Olive" title="b1">c1</font>, <font color="Olive" title="b2">c2</font>, <font color="Olive" title="b3">c3</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="b1">c1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b2">c2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">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="Olive" title="b1">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">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="b3">c3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</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="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">c1</font>, <font color="Maroon" title="c8">c2</font>, <font color="Maroon" title="c9">c3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E4:100"/><span class="lab"><font color="Green" title="E78">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">c1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c8">c2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c9">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E5:100"/><span class="lab"><font color="Green" title="E79">A4</font></span>: 
<font color="Maroon" title="c3">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="c7">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">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="c9">c3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:100"><span class="lab"><font color="Green" title="E77">A2</font></span></a></span>;<br/>
<a NAME="E6:100"/>
 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="c3">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">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</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">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b3">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b4">a3</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">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">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">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">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">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100"><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="c10">a1</font>, <font color="Maroon" title="c11">a2</font>, <font color="Maroon" title="c12">a3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E8:100"/><span class="lab"><font color="Green" title="E80">A5</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c11">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c12">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E9:100"/><span class="lab"><font color="Green" title="E81">A6</font></span>: 
<font color="Maroon" title="c3">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="c10">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">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="c12">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span>
 ;<br/>
<a NAME="E10:100"/><span class="lab"><font color="Green" title="E82">A7</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">c1</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="c11">a2</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">c2</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="c12">a3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">c3</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:100"><span class="lab"><font color="Green" title="E80">A5</font></span></a>, <a class="txt" href="#E4:100"><span class="lab"><font color="Green" title="E78">A3</font></span></a></span>;<br/>
 <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font> = 
<font color="Maroon" title="c3">x</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#T7" target="_self" title="EUCLIDLP:th.7">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">x2</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="c12">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">c2</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">x2</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">c3</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100"><span class="lab"><font color="Green" title="E81">A6</font></span></a>, <a class="txt" href="#E5:100"><span class="lab"><font color="Green" title="E79">A4</font></span></a>, <a class="ref" href="euclidlp.html#T19" target="_self" title="EUCLIDLP:th.19">Th19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">c1</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x1</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"><font color="Maroon" title="c11">a2</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">c2</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c5">x2</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"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">c3</font></span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c6">x3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#T29" target="_self" title="EUCLIDLP:th.29">Th29</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E12:100"/>
 <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</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="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:100"><span class="lab"><font color="Green" title="E82">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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