<?xml version="1.0"?>
<div class="add">

<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="E1:69"/><i><font color="Green">E35</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> &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> )
 ;<br/>

<a NAME="E2:69"/><i><font color="Green">E36</font></i>: 
0 <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E3:69"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E4:69"/><i><font color="Green">E38</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">y</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 
<b>by </b><i>, , <a class="ref" href="matrixc1.html#T6" target="_self">Th6</a></i>;<br/>
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8">)|</a></span> <a href="complex1.html#K15">*'</a>  = 
<span class="p1">(<span class="default"><a href="matrixc1.html#K6" target="_self">Sum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">y</font>,<span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> 
<b>by </b><i><a class="txt" href="matrixc1.html#E4:69"><i><font color="Green">E38</font></i></a>, </i>
<br/>.= 
 <a href="matrixc1.html#K6" target="_self">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">y</font>,<span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span> <a href="complsp2.html#K1">*'</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
 <a href="matrixc1.html#K6" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8">)|</a></span>
<b>by </b><i><a class="txt" href="matrixc1.html#E4:69"><i><font color="Green">E38</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E6:69"/>
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="complsp2.html#K8">)|</a></span> <a href="complex1.html#K15">*'</a> 
 ;<br/>


</div>
