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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>let </b><font color="Maroon">M</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><a NAME="E1:73"/><i><font color="Green">E35</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:73"/><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="matrixc1.html#T7" target="_self">Th7</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E3:73"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="matrixc1.html#K7" target="_self">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:73"/><i><font color="Green">E38</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="E5:73"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">y</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">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E6:73"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="matrix_1.html#D7">MATRIX_1:def 7</a></i>;<br/>
<a NAME="E7:73"/><i><font color="Green">E42</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E8:73"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">y</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">M</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, <a class="ref" href="complsp2.html#D1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E9:73"/><i><font color="Green">E53</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="matrix_1.html#K1">width</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, <a class="ref" href="complsp2.html#D1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E10:73"/><i><font color="Green">E54</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<font color="Maroon">M</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">M</font>
 
<b>by </b><i>, <a class="ref" href="matrixc1.html#T9" target="_self">Th9</a>, </i>;<br/>
<a NAME="E11:73"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixc1.html#K2" target="_self">@"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="matrixc1.html#K1" target="_self">*'</a> 
 
<b>by </b><i><a class="ref" href="matrix_2.html#T15">MATRIX_2:15</a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a></i>;<br/>
<b>thus </b><span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="matrixc1.html#K7" target="_self">*</a> <font color="Maroon">x</font></span>)</span>,<font color="Maroon">y</font></span><a href="complsp2.html#K8">)|</a></span> = 
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">y</font>,<span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="matrixc1.html#K7" target="_self">*</a> <font color="Maroon">x</font></span>)</span></span><a href="complsp2.html#K8">)|</a></span> <a href="complex1.html#K15">*'</a> 
<b>by </b><i><a class="txt" href="matrixc1.html#E10:73"><i><font color="Green">E54</font></i></a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="matrixc1.html#K7" target="_self">*</a> <font color="Maroon">x</font></span>)</span> <a href="complsp2.html#K1">*'</a> </span>)</span></span><a href="complsp2.html#K8">)|</a></span>
<b>by </b><i><a class="txt" href="matrixc1.html#E11:73"><i><font color="Green">E55</font></i></a>, , <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="matrixc1.html#K1" target="_self">*'</a> </span>)</span> <a href="matrixc1.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span></span><a href="complsp2.html#K8">)|</a></span>
<b>by </b><i><a class="txt" href="matrixc1.html#E6:73"><i><font color="Green">E41</font></i></a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
 <a href="matrixc1.html#K13" target="_self">SumAll</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, , , , , <a class="ref" href="matrixc1.html#T11" target="_self">Th11</a></i>
<br/>.= 
 <a href="matrixc1.html#K13" target="_self">SumAll</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_2.html#T15">MATRIX_2:15</a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a></i>
<br/>.= 
 <a href="matrixc1.html#K13" target="_self">SumAll</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<font color="Maroon">M</font>,<span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, <a class="ref" href="matrixc1.html#T10" target="_self">Th10</a></i>
<br/>.= 
 <a href="matrixc1.html#K13" target="_self">SumAll</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="matrixc1.html#K2" target="_self">@"</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span> <a href="matrixc1.html#K1" target="_self">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="matrixc1.html#T5" target="_self">Th5</a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, , </i>
<br/>.= 
 <a href="matrixc1.html#K13" target="_self">SumAll</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K4">@</a> </span>)</span>,<font color="Maroon">y</font></span>)</span> <a href="matrixc1.html#K1" target="_self">*'</a> </span>)</span> <a href="matrixc1.html#K1" target="_self">*'</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E9:73"><i><font color="Green">E53</font></i></a>, <a class="ref" href="matrixc1.html#T7" target="_self">Th7</a>, , </i>
<br/>.= 
 <a href="matrixc1.html#K13" target="_self">SumAll</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K14" target="_self">QuadraticForm</a> <font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K4">@</a> </span>)</span>,<font color="Maroon">y</font></span>)</span>
<b>by </b><i/>
;<br/>


</div>
