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<b>let </b><font color="Maroon" title="c1">a1</font>, <font color="Maroon" title="c2">a2</font>, <font color="Maroon" title="c3">a3</font>, <font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">b3</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font> being   <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> <br/> for <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">x3</font>, <font color="Olive" title="b5">x</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="Olive" title="b1">n</font>  st <font color="Olive" title="b2">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b3">x1</font>,<font color="Olive" title="b4">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b3">x1</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a>  &amp; <font color="Olive" title="b5">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="b2">x2</font>,<font color="Olive" title="b4">x3</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b5">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="c1">a1</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="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b2">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b4">x3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b5">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="c4">b1</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="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b2">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b4">x3</font></span>)</span> holds <br/>( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> )</span><br/><b>let </b><font color="Maroon" title="c7">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x2</font>, <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x</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="c7">n</font>  st <font color="Olive" title="b1">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b2">x1</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a>  &amp; <font color="Olive" title="b4">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="b1">x2</font>,<font color="Olive" title="b3">x3</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b4">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="c1">a1</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="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b1">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b3">x3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b4">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="c4">b1</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="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b1">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b3">x3</font></span>)</span> holds <br/>( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> )</span><br/><b>let </b><font color="Maroon" title="c8">x2</font>, <font color="Maroon" title="c9">x1</font>, <font color="Maroon" title="c10">x3</font>, <font color="Maroon" title="c11">x</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="c7">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font>,<font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a>  &amp; <font color="Maroon" title="c11">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="c9">x1</font>,<font color="Maroon" title="c8">x2</font>,<font color="Maroon" title="c10">x3</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c11">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="c1">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c11">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="c4">b1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> implies ( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> ) )</span><br/>





















<b>assume </b><a NAME="E1:100"/><i><font color="Green" title="E79">A1</font></i>: 
( <font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font>,<font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a>  &amp; <font color="Maroon" title="c11">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="c9">x1</font>,<font color="Maroon" title="c8">x2</font>,<font color="Maroon" title="c10">x3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <span class="p1">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c11">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="c1">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> or  not <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c11">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="c4">b1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> or ( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> ) )</span><br/>

<b>assume </b><a NAME="E2:100"/><i><font color="Green" title="E80">A2</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c11">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="c1">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c11">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="c4">b1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> )</span><br/>

<a NAME="E3:100"/><b>then </b>
<font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">a3</font>
 
;<br/>
<b>then </b><font color="Maroon" title="c11">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">1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E2:100"><i><font color="Green" title="E80">A2</font></i></a>, <a class="ref" href="euclidlp.html#T18" target="_self" title="EUCLIDLP:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" title="EUCLID_4:th.3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32" title="RVSUM_1:th.32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32" title="RVSUM_1:th.32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32" title="RVSUM_1:th.32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T8" target="_self" title="EUCLIDLP:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T8" target="_self" title="EUCLIDLP:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T6" title="EUCLID_4:th.6">EUCLID_4:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T6" title="EUCLID_4:th.6">EUCLID_4:6</a></i>
;<br/>
<a NAME="E5:100"/><b>then </b><i><font color="Green" title="E81">A3</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclidlp.html#T12" target="_self" title="EUCLIDLP:th.12">Th12</a></i>;<br/>
<font color="Maroon" title="c11">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">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c6">b3</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E2:100"><i><font color="Green" title="E80">A2</font></i></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="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T18" target="_self" title="EUCLIDLP:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" title="EUCLID_4:th.3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32" title="RVSUM_1:th.32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32" title="RVSUM_1:th.32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32" title="RVSUM_1:th.32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T8" target="_self" title="EUCLIDLP:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <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="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T8" target="_self" title="EUCLIDLP:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c10">x3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T6" title="EUCLID_4:th.6">EUCLID_4:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T6" title="EUCLID_4:th.6">EUCLID_4:6</a></i>
;<br/>
<a NAME="E7:100"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</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="c3">a3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</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="c6">b3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">x1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E5:100"><i><font color="Green" title="E81">A3</font></i></a>, <a class="ref" href="euclidlp.html#T12" target="_self" title="EUCLIDLP:th.12">Th12</a></i>;<br/>
<a NAME="E8:100"/><b>then </b>
( <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> )
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:100"><i><font color="Green" title="E79">A1</font></i></a>, <a class="ref" href="euclidlp.html#T40" target="_self" title="EUCLIDLP:th.40">Th40</a></i>;<br/>
<b>hence </b><a NAME="E9:100"/>
( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b3</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E2:100"><i><font color="Green" title="E80">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
