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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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="E1:36"/><i><font color="Green">E28</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;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<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/>
<b>reconsider </b><font color="Maroon">c<sub>5</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>6</sub></font> = <font color="Maroon">c<sub>3</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>3</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/>
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D7">COMPLSP1:def 7</a></i>
<br/>.= 
<a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D7">COMPLSP1:def 7</a></i>
<br/>.= 
<a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <span class="p1">(<span class="default"><a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="finseqop.html#T29">FINSEQOP:29</a>, <a class="txt" href="complsp2.html#E1:36"><i><font color="Green">E28</font></i></a></i>
<br/>.= 
<a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="complsp1.html#D7">COMPLSP1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="complsp1.html#D7">COMPLSP1:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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