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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:70"/><i><font color="Green">E56</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:70"/><i><font color="Green">E57</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">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:70"><i><font color="Green">E56</font></i></a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E3:70"/><i><font color="Green">E58</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></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">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1">COMPLSP2:def 1</a></i>;<br/>
<a NAME="E4:70"/><i><font color="Green">E59</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T18" target="_self">Th18</a>, <a class="txt" href="matrixc1.html#E1:70"><i><font color="Green">E56</font></i></a>, <a class="txt" href="matrixc1.html#E3:70"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E5:70"/><i><font color="Green">E60</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1">COMPLSP2:def 1</a></i>;<br/>
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span></span><a href="complsp2.html#K8">)|</a></span> = 
 <a href="matrixc1.html#K6" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixc1.html#T40" target="_self">Th40</a>, <a class="txt" href="matrixc1.html#E1:70"><i><font color="Green">E56</font></i></a>, <a class="txt" href="matrixc1.html#E3:70"><i><font color="Green">E58</font></i></a>, <a class="txt" href="matrixc1.html#E5:70"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
 <a href="matrixc1.html#K6" target="_self">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span> <a href="complsp2.html#K1">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="matrixc1.html#T28" target="_self">Th28</a>, <a class="txt" href="matrixc1.html#E1:70"><i><font color="Green">E56</font></i></a>, <a class="txt" href="matrixc1.html#E3:70"><i><font color="Green">E58</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrixc1.html#K6" target="_self">Sum</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K5" target="_self">mlt</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> 
<b>by </b><i><a class="ref" href="matrixc1.html#T24" target="_self">Th24</a>, <a class="txt" href="matrixc1.html#E2:70"><i><font color="Green">E57</font></i></a>, <a class="txt" href="matrixc1.html#E4:70"><i><font color="Green">E59</font></i></a></i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="complsp2.html#K8">)|</a></span> <a href="complex1.html#K15">*'</a> 
<b>by </b><i><a class="ref" href="matrixc1.html#T40" target="_self">Th40</a>, <a class="txt" href="matrixc1.html#E1:70"><i><font color="Green">E56</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E7:70"/>
<span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="complsp2.html#K8">)|</a></span> <a href="complex1.html#K15">*'</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp2.html#K8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp2.html#K1">*'</a> </span>)</span></span><a href="complsp2.html#K8">)|</a></span>
 ;<br/>


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