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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> ;<br/>





<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>1</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self">Def1</a></i>;<br/>
<b>assume </b><a NAME="E2:52"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1" target="_self">F_Complex</a> 
 ;<br/>

<b>assume </b><a NAME="E3:52"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:52_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="txt" href="complfld.html#E3:52"><i><font color="Green">E14</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1"><b>suppose </b></a><a NAME="E1:52_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:52_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="complfld.html#T6" target="_self">Th6</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="complfld.html#E2:52"><i><font color="Green">E13</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self">Th9</a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K5">/</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="complfld.html#E2:52"><i><font color="Green">E13</font></i></a>, <a class="ref" href="complfld.html#T8" target="_self">Th8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_2"><b>suppose </b></a><a NAME="E1:52_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:52_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="complfld.html#T6" target="_self">Th6</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="complfld.html#E2:52"><i><font color="Green">E13</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self">Th9</a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K5">/</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="complfld.html#E2:52"><i><font color="Green">E13</font></i></a>, <a class="ref" href="complfld.html#T8" target="_self">Th8</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

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