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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="E1:70"/><i><font color="Green" title="E53">A1</font></i>: 
(  <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="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="c1">x</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="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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:70"/><b>then </b><i><font color="Green" title="E54">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#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E3:70"/><i><font color="Green" title="E55">A3</font></i>: 
 <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="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="c3">M</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D7" target="_self" title="MATRIXC1:def.7">Def7</a></i>;<br/>
<a NAME="E4:70"/><i><font color="Green" title="E56">A4</font></i>: 
 <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="E5:70"/><i><font color="Green" title="E57">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</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="c2">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E6:70"/><i><font color="Green" title="E58">A6</font></i>: 
 <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> <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>
 
<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="E7:70"/><i><font color="Green" title="E59">A7</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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> <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>
 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="matrix_2.html#T12" title="MATRIX_2:th.12">MATRIX_2:12</a></i>;<br/>
<a NAME="E8:70"/><i><font color="Green" title="E60">A8</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</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="c3">M</font>
 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E9:70"/>
 <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="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E10:70"/><b>then </b><i><font color="Green" title="E61">A9</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#K13" title="MATRIXC1:func.13">QuadraticForm</a> <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>,<font color="Maroon" title="c3">M</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="c3">M</font>
 
<b>by </b><i><a class="txt" href="matrixc1.html#E8:70"><i><font color="Green" title="E60">A8</font></i></a>, <a class="ref" href="matrixc1.html#D13" target="_self" title="MATRIXC1:def.13">Def13</a></i>;<br/>
<a NAME="E11:70"/><i><font color="Green" title="E62">A10</font></i>: 
<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> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> 
 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="matrix_2.html#T15" title="MATRIX_2:th.15">MATRIX_2:15</a></i>;<br/>
<b>thus </b><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="c1">x</font></span>)</span>,<font color="Maroon" title="c2">y</font></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"><font color="Maroon" title="c2">y</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="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="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E3:70"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="matrixc1.html#T57" target="_self" title="MATRIXC1:th.57">Th57</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"><font color="Maroon" title="c2">y</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E3:70"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="matrixc1.html#T58" target="_self" title="MATRIXC1:th.58">Th58</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"><font color="Maroon" title="c2">y</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrixc1.html#K6" title="MATRIXC1:func.6">*</a> <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><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E2:70"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="matrixc1.html#T45" target="_self" title="MATRIXC1:th.45">Th45</a></i>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> <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 class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,<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>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E4:70"><i><font color="Green" title="E56">A4</font></i></a>, <a class="txt" href="matrixc1.html#E5:70"><i><font color="Green" title="E57">A5</font></i></a>, <a class="txt" href="matrixc1.html#E6:70"><i><font color="Green" title="E58">A6</font></i></a>, <a class="txt" href="matrixc1.html#E7:70"><i><font color="Green" title="E59">A7</font></i></a>, <a class="txt" href="matrixc1.html#E11:70"><i><font color="Green" title="E62">A10</font></i></a>, <a class="ref" href="matrixc1.html#T60" target="_self" title="MATRIXC1:th.60">Th60</a></i>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> <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>,<font color="Maroon" title="c3">M</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>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="matrix_2.html#T15" title="MATRIX_2:th.15">MATRIX_2:15</a></i>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span>,<font color="Maroon" title="c3">M</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="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E10:70"><i><font color="Green" title="E61">A9</font></i></a>, <a class="ref" href="matrixc1.html#T54" target="_self" title="MATRIXC1:th.54">Th54</a></i>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> <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 class="p3">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E4:70"><i><font color="Green" title="E56">A4</font></i></a>, <a class="txt" href="matrixc1.html#E5:70"><i><font color="Green" title="E57">A5</font></i></a>, <a class="ref" href="matrixc1.html#T55" target="_self" title="MATRIXC1:th.55">Th55</a></i>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,<font color="Maroon" title="c2">y</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="matrixc1.html#E6:70"><i><font color="Green" title="E58">A6</font></i></a>, <a class="txt" href="matrixc1.html#E7:70"><i><font color="Green" title="E59">A7</font></i></a>, <a class="ref" href="matrixc1.html#T56" target="_self" title="MATRIXC1:th.56">Th56</a></i>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,<font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="matrixc1.html#T2" target="_self" title="MATRIXC1:th.2">Th2</a></i>
;<br/>


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