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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="rvsum_1.html#V1" target="_self">complex-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<a NAME="E1:106"/><i><font color="Green">E67</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K2">COMPLEX</a>  &amp;  <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="rvsum_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E2:106"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="rvsum_1.html#D11" target="_self">Def11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="txt" href="rvsum_1.html#E1:106"><i><font color="Green">E67</font></i></a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>thus </b> <a href="rvsum_1.html#K16" target="_self">Product</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<a href="binop_2.html#K29">multcomplex</a>  <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="rvsum_1.html#D12" target="_self">Def12</a></i>
<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K29">multcomplex</a>  <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K29">multcomplex</a>  <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finsop_1.html#T6">FINSOP_1:6</a></i>
<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" target="_self">Product</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K29">multcomplex</a>  <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#D12" target="_self">Def12</a></i>
<br/>.= 
<a href="binop_2.html#K29">multcomplex</a>  <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" target="_self">Product</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rvsum_1.html#K17" target="_self">Product</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#D12" target="_self">Def12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K16" target="_self">Product</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" target="_self">Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rvsum_1.html#E2"><i><font color="Green">Lemma2</font></i></a></i>
;<br/>


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