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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>let </b><font color="Maroon" title="c3">M</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>



<b>assume </b><a NAME="E1:74"/><i><font color="Green" title="E57">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="c3">M</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 ;<br/>

<i><font color="Green" title="E58">A2</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a> </span>)</span> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c1">x</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a> </span>)</span>
<b>by </b><i><a class="ref" href="matrixc1.html#D7" target="_self" title="MATRIXC1:def.7">Def7</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></i>
;<br/>
<a NAME="E3:74"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c2">y</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="txt" href="matrixc1.html#E1:74"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="matrixc1.html#D7" target="_self" title="MATRIXC1:def.7">Def7</a></i>;<br/>
<b>hence </b><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="c3">M</font> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> = 
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c2">y</font></span>)</span>,<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> 
<b>by </b><i><a class="ref" href="matrixc1.html#T57" target="_self" title="MATRIXC1:th.57">Th57</a>, <a class="txt" href="matrixc1.html#E1:74"><i><font color="Green" title="E57">A1</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="c2">y</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a> </span>)</span> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="ref" href="matrixc1.html#T62" target="_self" title="MATRIXC1:th.62">Th62</a>, <a class="txt" href="matrixc1.html#E1:74"><i><font color="Green" title="E57">A1</font></i></a></i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a> </span>)</span> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c1">x</font></span>)</span>,<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#E2:74"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="matrixc1.html#E1:74"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="matrixc1.html#T57" target="_self" title="MATRIXC1:th.57">Th57</a></i>
;<br/><br/>


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