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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="E1:41"/><i><font color="Green">E32</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; <font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K11">0c</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E4:41"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="complsp1.html#D7">COMPLSP1:def 7</a></i>;<br/>
<a NAME="E5:41"/><i><font color="Green">E34</font></i>: 
 <a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K25">compcomplex</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="complsp1.html#D9">COMPLSP1:def 9</a></i>;<br/>
<a NAME="E6:41"/><i><font color="Green">E35</font></i>: 
 <a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K25">compcomplex</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="complsp1.html#D9">COMPLSP1:def 9</a></i>;<br/>
<a NAME="E7:41"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complsp2.html#K9" target="_self">|-&gt;</a> <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i><a class="ref" href="complsp1.html#D13">COMPLSP1:def 13</a>, <a class="txt" href="complsp2.html#E1:41"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E8:41"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp2.html#K5" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="complsp1.html#T7">COMPLSP1:7</a>, <a class="ref" href="complsp1.html#T8">COMPLSP1:8</a>, <a class="ref" href="binop_2.html#T1">BINOP_2:1</a>, <a class="ref" href="finseqop.html#T78">FINSEQOP:78</a>, <a class="txt" href="complsp2.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="complsp2.html#E4:41"><i><font color="Green">E33</font></i></a>, <a class="txt" href="complsp2.html#E6:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="complsp2.html#E7:41"><i><font color="Green">E36</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:41"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="complsp1.html#T7">COMPLSP1:7</a>, <a class="ref" href="complsp1.html#T8">COMPLSP1:8</a>, <a class="ref" href="binop_2.html#T1">BINOP_2:1</a>, <a class="ref" href="finseqop.html#T78">FINSEQOP:78</a>, <a class="txt" href="complsp2.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="complsp2.html#E4:41"><i><font color="Green">E33</font></i></a>, <a class="txt" href="complsp2.html#E5:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="complsp2.html#E7:41"><i><font color="Green">E36</font></i></a></i>;<br/>


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