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

<b>assume </b><a NAME="E1:37"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</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">x</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">y'</font> = <font color="Maroon">y</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">y</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">x</font> <a href="complsp1.html#K3">+</a> <font color="Maroon">y</font> = 
<a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<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">y'</font>,<font color="Maroon">x'</font>
<b>by </b><i><a class="ref" href="finseqop.html#T34">FINSEQOP:34</a>, <a class="ref" href="complsp2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<font color="Maroon">y</font> <a href="complsp1.html#K3">+</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="complsp1.html#D7">COMPLSP1:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E5:37"/>
<font color="Maroon">x</font> <a href="complsp1.html#K3">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="complsp1.html#K3">+</a> <font color="Maroon">x</font>
 ;<br/>


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