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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">y2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:83"/><i><font color="Green" title="E72">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y2</font> )
 ;<br/>

<a NAME="E2:83"/><i><font color="Green" title="E73">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y1</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E3:83"/><i><font color="Green" title="E74">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y2</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E4:83"/><i><font color="Green" title="E75">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E5:83"/><i><font color="Green" title="E76">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y1</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E6:83"/><i><font color="Green" title="E77">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y2</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E7:83"/><i><font color="Green" title="E78">A7</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T52" target="_self" title="COMPLSP2:th.52">Th52</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T52" target="_self" title="COMPLSP2:th.52">Th52</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T52" target="_self" title="COMPLSP2:th.52">Th52</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T52" target="_self" title="COMPLSP2:th.52">Th52</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</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"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_2.html#T28" title="EUCLID_2:th.28">EUCLID_2:28</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:83"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="complsp2.html#E3:83"><i><font color="Green" title="E74">A3</font></i></a>, <a class="txt" href="complsp2.html#E4:83"><i><font color="Green" title="E75">A4</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"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T28" title="EUCLID_2:th.28">EUCLID_2:28</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="complsp2.html#E5:83"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="complsp2.html#E6:83"><i><font color="Green" title="E77">A6</font></i></a>, <a class="txt" href="complsp2.html#E7:83"><i><font color="Green" title="E78">A7</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"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T28" title="EUCLID_2:th.28">EUCLID_2:28</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="complsp2.html#E4:83"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="complsp2.html#E5:83"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="complsp2.html#E6:83"><i><font color="Green" title="E77">A6</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"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">y1</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T28" title="EUCLID_2:th.28">EUCLID_2:28</a>, <a class="txt" href="complsp2.html#E1:83"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:83"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="complsp2.html#E3:83"><i><font color="Green" title="E74">A3</font></i></a>, <a class="txt" href="complsp2.html#E7:83"><i><font color="Green" title="E78">A7</font></i></a></i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y1</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">y2</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>

;<br/>
<b>hence </b><a NAME="E9:83"/>
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">y1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">y2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y1</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">y2</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
 ;<br/>


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