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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">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> ;<br/>





<b>assume </b><a NAME="E1:3"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c1">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"><font color="Maroon" title="c2">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">r1</font> = <font color="Maroon" title="c2">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font>;<br/>
<b>set </b><font color="Maroon" title="c5">r2</font> = <font color="Maroon" title="c3">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font>;<br/>
<a NAME="E2:3"/>
( <font color="Maroon" title="c2">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c1">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"><font color="Maroon" title="c2">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="complsp2.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="complsp1.html#D7" title="COMPLSP1:def.7">COMPLSP1:def 7</a></i>;<br/>
<a NAME="E3:3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>;<br/>
<b>hence </b><a NAME="E4:3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="binop_2.html#D3" title="BINOP_2:def.3">BINOP_2:def 3</a></i>;<br/>


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