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<b>let </b><font color="Maroon" title="c1">x</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>let </b><font color="Maroon" title="c2">c</font> be  <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>reconsider </b><font color="Maroon" title="c3">cc</font> = <font color="Maroon" title="c2">c</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></i>;<br/>
<a NAME="E2:41"/><i><font color="Green" title="E31">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p2">(<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></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>
<font color="Maroon" title="c2">c</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p2">(<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></span>)</span> = 
<span class="p1">(<span class="default"><a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> <font color="Maroon" title="c3">cc</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span></span>)</span> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p2">(<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></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>
<br/>.= 
<a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="finseqop.html#K3" title="FINSEQOP:func.3">[;]</a> <font color="Maroon" title="c3">cc</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p3">(<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></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T44" title="FUNCOP_1:th.44">FUNCOP_1:44</a></i>
<br/>.= 
<a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="finseqop.html#K3" title="FINSEQOP:func.3">[;]</a> <font color="Maroon" title="c3">cc</font>,<span class="p1">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p2">(<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></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E2:41"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="relat_1.html#T79" title="RELAT_1:th.79">RELAT_1:79</a></i>
<br/>.= 
<a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="finseqop.html#K3" title="FINSEQOP:func.3">[;]</a> <font color="Maroon" title="c3">cc</font>,<span class="p1">(<span class="default"><span class="p2">(<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="complsp2.html#K9" title="COMPLSP2:func.9">|-&gt;</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span>
<b>by </b><i><a class="ref" href="complsp1.html#D13" title="COMPLSP1:def.13">COMPLSP1:def 13</a></i>
<br/>.= 
<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="complsp2.html#K9" title="COMPLSP2:func.9">|-&gt;</a> <span class="p1">(<span class="default"><a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">cc</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T19" title="FINSEQOP:th.19">FINSEQOP:19</a></i>
<br/>.= 
<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="complsp2.html#K9" title="COMPLSP2:func.9">|-&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">cc</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D5" title="BINOP_2:def.5">BINOP_2:def 5</a></i>
<br/>.= 
 <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <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>
<b>by </b><i><a class="ref" href="complsp1.html#D13" title="COMPLSP1:def.13">COMPLSP1:def 13</a></i>
;<br/>
<b>hence </b><a NAME="E4:41"/>
<font color="Maroon" title="c2">c</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <span class="p1">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p2">(<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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <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>
 ;<br/>


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