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<b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">y</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:88"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 ;<br/>

<b>set </b><font color="Maroon">z</font> = <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>;<br/>
<span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp1.html#K4">-</a> <font color="Maroon">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp1.html#K4">-</a> <font color="Maroon">y</font></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="binop_2.html#K4">-</a> <span class="p3"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span> <a href="binop_2.html#K4">-</a> <span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span> <a href="binop_2.html#K3">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T16" target="_self">Th16</a>, <a class="ref" href="complsp2.html#T17" target="_self">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="binop_2.html#K4">-</a> <span class="p3"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span> <a href="binop_2.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="binop_2.html#K3">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>
<b>by </b><i>, <a class="ref" href="complsp2.html#T17" target="_self">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="binop_2.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="binop_2.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K3">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p4"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:88"/>
<span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp1.html#K4">-</a> <font color="Maroon">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp1.html#K4">-</a> <font color="Maroon">y</font></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p4"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>
 ;<br/>


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