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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:51"/><i><font color="Green">E43</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <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/>
<b>thus </b><a href="complex1.html#K5">0c</a>  <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><a href="binop_2.html#K29">multcomplex</a>  <a href="funcop_1.html#K8">[;]</a> <a href="complex1.html#K5">0c</a> ,<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> <font color="Maroon">c<sub>2</sub></font>

<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="finseqop.html#K3">[;]</a> <a href="complex1.html#K5">0c</a> ,<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> <font color="Maroon">c<sub>2</sub></font></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> <a href="complex1.html#K5">0c</a> ,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="complsp1.html#E1:51"><i><font color="Green">E43</font></i></a>, <a class="ref" href="relat_1.html#T79">RELAT_1:79</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="finseqop.html#K4">|-&gt;</a> <a href="complex1.html#K5">0c</a> 
<b>by </b><i><a class="txt" href="complsp1.html#E4"><i><font color="Green">Lemma2</font></i></a>, <a class="ref" href="complsp1.html#T7" target="_self">Th7</a>, <a class="ref" href="complsp1.html#T15" target="_self">Th15</a>, <a class="ref" href="finseqop.html#T80">FINSEQOP:80</a></i>
<br/>.= 
 <a href="complsp1.html#K11" target="_self">0c</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>


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