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<b>let </b><font color="Maroon" title="c1">F1</font>, <font color="Maroon" title="c2">F2</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="E1:40"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">F1</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">F2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">x2</font> = <font color="Maroon" title="c1">F1</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">F1</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">y2</font> = <font color="Maroon" title="c2">F2</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">F2</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/>
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">F2</font></span>)</span> = 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c1">F1</font>,<font color="Maroon" title="c2">F2</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D8" title="COMPLSP1:def.8">COMPLSP1:def 8</a></i>
<br/>.= 
<a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c3">x2</font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c4">y2</font></span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:40"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="complsp1.html#T7" title="COMPLSP1:th.7">COMPLSP1:7</a>, <a class="ref" href="complsp1.html#T8" title="COMPLSP1:th.8">COMPLSP1:8</a>, <a class="ref" href="complsp1.html#D3" title="COMPLSP1:def.3">COMPLSP1:def 3</a>, <a class="ref" href="setwop_2.html#T48" title="SETWOP_2:th.48">SETWOP_2:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c1">F1</font></span>)</span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">F2</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D4" title="BINOP_2:def.4">BINOP_2:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E5:40"/>
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F1</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">F2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c1">F1</font></span>)</span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">F2</font></span>)</span>
 ;<br/>


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