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<span class="kw">let </span><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</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> 3; <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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></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="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></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"><font color="Maroon" title="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span></span><br/>



<a NAME="E1:63"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
( <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<a NAME="E2:63"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
( <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<a NAME="E3:63"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
( <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<a NAME="E4:63"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T27" title="RVSUM_1:th.27">RVSUM_1:27</a></span>;<br/>
<a NAME="E5:63"/><span class="lab"><font color="Green" title="E29">A5</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T27" title="RVSUM_1:th.27">RVSUM_1:27</a></span>;<br/>
<a NAME="E6:63"/><span class="lab"><font color="Green" title="E30">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T27" title="RVSUM_1:th.27">RVSUM_1:27</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A7</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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></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"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></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"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="euclid_8.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></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"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="euclid_8.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> 1</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="txt" href="euclid_8.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>

;<br/>
<a NAME="E8:63"/><span class="lab"><font color="Green" title="E32">A8</font></span>: 
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<a NAME="E9:63"/><span class="lab"><font color="Green" title="E33">A9</font></span>: 
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<a NAME="E10:63"/><span class="lab"><font color="Green" title="E34">A10</font></span>: 
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<span class="lab"><font color="Green" title="E35">A11</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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></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"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span> = 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:63"><span class="lab"><font color="Green" title="E31">A7</font></span></a>, <a class="txt" href="#E8:63"><span class="lab"><font color="Green" title="E32">A8</font></span></a>, <a class="txt" href="#E9:63"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="txt" href="euclid_8.html#E3"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>
<br/>.= 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>

;<br/>
<a NAME="E12:63"/>
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<span class="kw">then </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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></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"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span> = 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><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="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63"><span class="lab"><font color="Green" title="E34">A10</font></span></a>, <a class="txt" href="#E11:63"><span class="lab"><font color="Green" title="E35">A11</font></span></a>, <a class="txt" href="euclid_8.html#E3"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>
<br/>.= 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>

;<br/>
<span class="kw">hence </span><a NAME="E14:63"/>
<font color="Maroon" title="c1">p1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></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="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></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"><font color="Maroon" title="c1">p1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3</span>)</span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="txt" href="#E6:63"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="ref" href="euclid_8.html#T1" target="_self" title="EUCLID_8:th.1">Th1</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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