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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <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>  st  <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="Olive" title="b1">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="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">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>  holds <br/><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"><span class="p3">(<span class="default"><font color="Olive" title="b1">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="c2">y</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="Olive" title="b1">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></span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <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="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="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>  implies <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"><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="c2">y</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:69"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 <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>
 <span class="kw">and </span><br/><a NAME="E2:69"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
 <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>
 <span class="kw">and </span><br/><a NAME="E3:69"/><span class="lab"><font color="Green" title="E54">A3</font></span>: 
 <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> 
 <span class="kw">and </span><br/><a NAME="E4:69"/><span class="lab"><font color="Green" title="E55">A4</font></span>: 
 <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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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"><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="c2">y</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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></span><br/>

<a NAME="E5:69"/><span class="lab"><font color="Green" title="E56">A5</font></span>: 
 <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="c2">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="txt" href="#E3:69"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></span>;<br/>
<a NAME="E6:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A6</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><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> <a href="matrixc1.html#K1" title="MATRIXC1: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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></span>;<br/>
<span class="lab"><font color="Green" title="E58">A7</font></span>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> = 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <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></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#D9" target="_self" title="MATRIXC1:def.9">Def10</a></span>
;<br/>
<a NAME="E8:69"/><span class="lab"><font color="Green" title="E59">A8</font></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="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="c1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="matrix_1.html#D6" title="MATRIX_1:def.6">MATRIX_1:def 6</a></span>;<br/>
<span class="lab"><font color="Green" title="E60">A9</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> = 
 <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> (<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#D9" target="_self" title="MATRIXC1:def.9">Def10</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E5:69"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="matrixc1.html#D12" target="_self" title="MATRIXC1:def.12">Def13</a></span>
;<br/>
<span class="lab"><font color="Green" title="E61">A10</font></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> = 
 <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="matrix_1.html#D6" title="MATRIX_1:def.6">MATRIX_1:def 6</a></span>
;<br/>
<a NAME="E11:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A11</font></span>: 
 <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="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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#D6" target="_self" title="MATRIXC1:def.6">Def7</a></span>;<br/>
<a NAME="E12:69"/><span class="kw">then </span>
 <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"><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="c2">y</font></span>)</span> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></span>;<br/>
<a NAME="E13:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A12</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</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> <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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:69"><span class="lab"><font color="Green" title="E60">A9</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>;<br/>
<a NAME="E14:69"/><span class="lab"><font color="Green" title="E64">A13</font></span>: 
<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="c2">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E15:69"/>
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <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> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font> &amp; <font color="Maroon" title="c4">i</font> <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> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:69_4"/><span class="lab"><font color="Green" title="E65">A14</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">and </span><br/><a NAME="E2:69_4"/><span class="lab"><font color="Green" title="E66">A15</font></span>: 
<font color="Maroon" title="c4">i</font> <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> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span><br/>

<span class="lab"><font color="Green" title="E67">A16</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> = 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E5:69"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="matrixc1.html#D12" target="_self" title="MATRIXC1:def.12">Def13</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>
;<br/>
<a NAME="E4:69_4"/><span class="lab"><font color="Green" title="E68">A17</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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>,<font color="Maroon" title="c4">i</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="c2">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:69"><span class="lab"><font color="Green" title="E57">A6</font></span></a>, <a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>;<br/>
<a NAME="E5:69_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A18</font></span>: 
 <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> (<span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:69"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>;<br/>
<a NAME="E6:69_4"/>
 <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="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> (<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E5:69"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="matrixc1.html#D12" target="_self" title="MATRIXC1:def.12">Def13</a></span>;<br/>
<a NAME="E7:69_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A19</font></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="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> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#D9" target="_self" title="MATRIXC1:def.9">Def10</a></span>;<br/>
<a NAME="E8:69_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A20</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <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></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E10:69"><span class="lab"><font color="Green" title="E61">A10</font></span></a>, <a class="txt" href="#E1:69_4"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E2:69_4"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E9:69_4"/><span class="lab"><font color="Green" title="E72">A21</font></span>: 
 for <font color="Olive" title="b1">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b1">j</font> <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> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">j</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_4_2"><span class="kw">proof </span></a><div class="add">

<span class="lab"><font color="Green" title="E73">A22</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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="c4">i</font>)</span>)</span> = 
 <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="txt" href="#E3:69"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></span>
<br/>.= 
 <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></span>
;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">j</font> &amp; <font color="Maroon" title="c5">j</font> <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> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:69_4_2"/><span class="lab"><font color="Green" title="E74">A23</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">j</font>
 <span class="kw">and </span><br/><a NAME="E3:69_4_2"/><span class="lab"><font color="Green" title="E75">A24</font></span>: 
<font color="Maroon" title="c5">j</font> <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> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span><br/>

<a NAME="E4:69_4_2"/><span class="lab"><font color="Green" title="E76">A25</font></span>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <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></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:69"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="txt" href="#E3:69_4"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E2:69_4_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="txt" href="#E3:69_4_2"><span class="lab"><font color="Green" title="E75">A24</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E5:69_4_2"/>
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_4"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E2:69_4_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="txt" href="#E3:69_4_2"><span class="lab"><font color="Green" title="E75">A24</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E6:69_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></span>;<br/>
<a NAME="E7:69_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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="c4">i</font>)</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></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_4_2"><span class="lab"><font color="Green" title="E73">A22</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>;<br/>
<a NAME="E8:69_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A26</font></span>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E9:69_4_2"/>
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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>,<font color="Maroon" title="c4">i</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69_4_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="txt" href="#E3:69_4_2"><span class="lab"><font color="Green" title="E75">A24</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E10:69_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A27</font></span>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>;<br/>
<a NAME="E11:69_4_2"/>
<font color="Maroon" title="c5">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="txt" href="#E3:69"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="txt" href="#E3:69_4"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E3:69_4_2"><span class="lab"><font color="Green" title="E75">A24</font></span></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></span>;<br/>
<a NAME="E12:69_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A28</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_4"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E2:69_4"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="txt" href="#E7:69_4"><span class="lab"><font color="Green" title="E70">A19</font></span></a>, <a class="txt" href="#E2:69_4_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="ref" href="matrixc1.html#T1" target="_self" title="MATRIXC1:th.1">Th1</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T16" title="COMPLSP2:th.16">COMPLSP2:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</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="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_4"><span class="lab"><font color="Green" title="E68">A17</font></span></a>, <a class="ref" href="matrixc1.html#T27" target="_self" title="MATRIXC1:th.27">Th28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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="c4">i</font>)</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="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E10:69"><span class="lab"><font color="Green" title="E61">A10</font></span></a>, <a class="txt" href="#E8:69_4"><span class="lab"><font color="Green" title="E71">A20</font></span></a>, <a class="ref" href="matrixc1.html#T41" target="_self" title="MATRIXC1:th.41">Th43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p2">(<span class="default"><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> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69_4_2"><span class="lab"><font color="Green" title="E77">A26</font></span></a>, <a class="ref" href="matrixc1.html#T18" target="_self" title="MATRIXC1:th.18">Th19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_4"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E2:69_4_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="txt" href="#E3:69_4_2"><span class="lab"><font color="Green" title="E75">A24</font></span></a>, <a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <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#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font>)</span>)</span></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_4_2"><span class="lab"><font color="Green" title="E76">A25</font></span></a>, <a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>
<br/>.= 
<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> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E5:69"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="txt" href="#E12:69_4_2"><span class="lab"><font color="Green" title="E79">A28</font></span></a>, <a class="ref" href="matrixc1.html#D12" target="_self" title="MATRIXC1:def.12">Def13</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E14:69_4_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c5">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:69_4_2"><span class="lab"><font color="Green" title="E78">A27</font></span></a>, <a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:69_4"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <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></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_4"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E2:69_4"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E11:69_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A29</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E12:69_4"/><span class="lab"><font color="Green" title="E74">A30</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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>,<font color="Maroon" title="c4">i</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="c2">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:69"><span class="lab"><font color="Green" title="E57">A6</font></span></a>, <a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a></span>;<br/>
<span class="lab"><font color="Green" title="E75">A31</font></span>:  <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="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span> = 
 <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"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T3" title="COMPLSP2:th.3">COMPLSP2:3</a></span>
<br/>.= 
 <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> (<span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<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>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_4"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E12:69_4"><span class="lab"><font color="Green" title="E74">A30</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>
;<br/>
<a NAME="E14:69_4"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:69"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="txt" href="#E1:69_4"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E2:69_4"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E15:69_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">then </span><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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#T18" target="_self" title="MATRIXC1:th.18">Th19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:69"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="txt" href="#E9:69"><span class="lab"><font color="Green" title="E60">A9</font></span></a>, <a class="txt" href="#E1:69_4"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E2:69_4"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="ref" href="complsp2.html#D1" title="COMPLSP2:def.1">COMPLSP2:def 1</a></span>
;<br/>
<span class="kw">then </span><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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:69_4"><span class="lab"><font color="Green" title="E71">A20</font></span></a>, <a class="ref" href="matrixc1.html#D6" target="_self" title="MATRIXC1:def.6">Def7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</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"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:69_4"><span class="lab"><font color="Green" title="E69">A18</font></span></a>, <a class="ref" href="matrixc1.html#T23" target="_self" title="MATRIXC1:th.23">Th24</a></span>
<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"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> (<span class="p4">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrixc1.html#K2" title="MATRIXC1:func.2">@"</a></span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>,<font color="Maroon" title="c2">y</font>)</span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#T28" target="_self" title="MATRIXC1:th.28">Th29</a></span>
;<br/>
<a NAME="E18:69_4"/><span class="kw">then </span>
<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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:69_4"><span class="lab"><font color="Green" title="E75">A31</font></span></a>, <a class="txt" href="#E9:69_4"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:69_4"/>
<span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:69"><span class="lab"><font color="Green" title="E58">A7</font></span></a>, <a class="txt" href="#E11:69_4"><span class="lab"><font color="Green" title="E73">A29</font></span></a>, <a class="ref" href="matrixc1.html#D9" target="_self" title="MATRIXC1:def.9">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E16:69"/><span class="kw">then </span>
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K10" title="MATRIXC1:func.10">LineSum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K13" title="MATRIXC1:func.13">QuadraticForm</a> (<font color="Maroon" title="c1">x</font>,<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>,<font color="Maroon" title="c2">y</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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"><span class="p3">(<span class="default"><span class="p4">(<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="c2">y</font></span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:69"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:69"/>
<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"><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="c2">y</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:69"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="ref" href="matrixc1.html#T39" target="_self" title="MATRIXC1:th.39">Th40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
