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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="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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/>







<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> ;<br/>
<a NAME="E1:49"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a>  <a href="binop_1.html#R7">is_distributive_wrt</a>  <a href="binop_2.html#K27">addcomplex</a> 
 
<b>by </b><i><a class="ref" href="complsp1.html#T17" target="_self">Th17</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K14" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complsp1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complsp1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="complsp1.html#E1:49"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseqop.html#T52">FINSEQOP:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complsp1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complsp1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complsp1.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

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