<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:14_2_1"/>
 <a href="binop_2.html#K29" target="_self">multcomplex</a>  is <a href="binop_1.html#V1">commutative</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D13">BINOP_1:def 13</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>thus </b><a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K5" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="binop_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="binop_2.html#D5" target="_self">Def5</a></i>
;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D14">BINOP_1:def 14</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>





<b>thus </b><a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_2.html#K5" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K5" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_2.html#K5" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_2.html#K5" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binop_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K29" target="_self">multcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binop_2.html#D5" target="_self">Def5</a></i>
;<br/>


</div>
