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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</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="E1:66"/><i><font color="Green" title="E50">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">y</font> &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> )
 ;<br/>

<a NAME="E2:66"/><b>then </b><i><font color="Green" title="E51">A2</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/>
<a NAME="E3:66"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </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#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E4:66"/><b>then </b><i><font color="Green" title="E52">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c2">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span></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">y</font>
 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:66"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="finseq_2.html#T86" title="FINSEQ_2:th.86">FINSEQ_2:86</a></i>;<br/>
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a>  = 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c2">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:66"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="matrixc1.html#T40" target="_self" title="MATRIXC1:th.40">Th40</a></i>
<br/>.= 
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c2">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:66"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="matrixc1.html#E2:66"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="matrixc1.html#E4:66"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="matrixc1.html#T24" target="_self" title="MATRIXC1:th.24">Th24</a></i>
<br/>.= 
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:66"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="matrixc1.html#T25" target="_self" title="MATRIXC1:th.25">Th25</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">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:66"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="matrixc1.html#T40" target="_self" title="MATRIXC1:th.40">Th40</a></i>
;<br/>
<b>hence </b><a NAME="E6:66"/>
<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">y</font></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="c2">y</font>,<font color="Maroon" title="c1">x</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
 ;<br/>


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