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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> ;<br/><b>let </b><font color="Maroon">c</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>reconsider </b><font color="Maroon">cc</font> = <font color="Maroon">c</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="xcmplx_0.html#D2">XCMPLX_0:def 2</a></i>;<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/>
<a NAME="E3:50"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11">0c</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<font color="Maroon">c</font> <a href="complsp1.html#K6">*</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11">0c</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="binop_2.html#K29">multcomplex</a>  <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">cc</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K2">COMPLEX</a> </span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11">0c</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="finseqop.html#K3">[;]</a> <font color="Maroon">cc</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K2">COMPLEX</a> </span>)</span> <a href="finseqop.html#K5">*</a> <span class="p2">(<span class="default"><a href="complsp1.html#K11">0c</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T44">FUNCOP_1:44</a></i>
<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="finseqop.html#K3">[;]</a> <font color="Maroon">cc</font>,<span class="p1">(<span class="default"><a href="complsp1.html#K11">0c</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T79">RELAT_1:79</a></i>
<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="finseqop.html#K3">[;]</a> <font color="Maroon">cc</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span> <a href="complsp2.html#K9" target="_self">|-&gt;</a> <a href="complex1.html#K5">0c</a> </span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D13">COMPLSP1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span> <a href="complsp2.html#K9" target="_self">|-&gt;</a> <span class="p1">(<span class="default"><a href="binop_2.html#K29">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">cc</font>,<a href="complex1.html#K5">0c</a> </span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T19">FINSEQOP:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span> <a href="complsp2.html#K9" target="_self">|-&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">cc</font> <a href="binop_2.html#K5">*</a> <a href="complex1.html#K5">0c</a> </span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D5">BINOP_2:def 5</a></i>
<br/>.= 
 <a href="complsp1.html#K11">0c</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D13">COMPLSP1:def 13</a></i>
;<br/>
<b>hence </b><a NAME="E5:50"/>
<font color="Maroon">c</font> <a href="complsp1.html#K6">*</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11">0c</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K11">0c</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span>
 ;<br/>


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