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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">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="E1:39"/><i><font color="Green" title="E31">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">x'</font> = <font color="Maroon" title="c1">x</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">y'</font> = <font color="Maroon" title="c2">y</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font> = 
<a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>
<b>by </b><i><a class="ref" href="complsp1.html#D8" title="COMPLSP1:def.8">COMPLSP1:def 8</a></i>
<br/>.= 
<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="c3">x'</font>,<span class="p1">(<span class="default"><a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a>  <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c4">y'</font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:39"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="complsp1.html#D3" title="COMPLSP1:def.3">COMPLSP1:def 3</a>, <a class="ref" href="finseqop.html#T89" title="FINSEQOP:th.89">FINSEQOP:89</a></i>
<br/>.= 
<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="c1">x</font>,<span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D9" title="COMPLSP1:def.9">COMPLSP1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D7" title="COMPLSP1:def.7">COMPLSP1:def 7</a></i>
;<br/>


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