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<b>let </b><font color="Maroon" title="c1">z2</font>, <font color="Maroon" title="c2">z1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/>



<b>reconsider </b><font color="Maroon" title="c3">z1'</font> = <font color="Maroon" title="c2">z1</font>, <font color="Maroon" title="c4">z2'</font> = <font color="Maroon" title="c1">z2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self" title="COMPLFLD:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E2:17"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c1">z2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/>

<b>assume </b><a NAME="E3:17"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c2">z1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  or <font color="Maroon" title="c1">z2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1"/>
( <font color="Maroon" title="c2">z1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  or <font color="Maroon" title="c1">z2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  )
 </span><b>by </b><i><a class="txt" href="complfld.html#E3:17"><i><font color="Green" title="E10">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>suppose </b></a><a NAME="E1:17_1_1"/>
<font color="Maroon" title="c2">z1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/><div class="add"><a NAME="E2:17_1_1"/><b>then </b><i><font color="Green" title="E11">A3</font></i>: 
<font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c4">z2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> 
 <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self" title="COMPLFLD:def.1">Def1</a></i>;<br/><a NAME="E3:17_1_1"/>
<font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z2'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 <b>by </b><i><a class="txt" href="complfld.html#E2:17"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="complfld.html#T7" target="_self" title="COMPLFLD:th.7">Th7</a></i>;<br/><b>hence </b><a NAME="E4:17_1_1"/>
<font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> 
 <b>by </b><i><a class="txt" href="complfld.html#E2:17"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="complfld.html#E2:17_1_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self" title="COMPLFLD:th.9">Th9</a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_2"><b>suppose </b></a><a NAME="E1:17_1_2"/>
<font color="Maroon" title="c1">z2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/><div class="add"><a NAME="E2:17_1_2"/><b>then </b><i><font color="Green" title="E11">A4</font></i>: 
<font color="Maroon" title="c4">z2'</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c3">z1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> 
 <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self" title="COMPLFLD:def.1">Def1</a></i>;<br/><a NAME="E3:17_1_2"/>
<font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z2'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 <b>by </b><i><a class="txt" href="complfld.html#E2:17"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="complfld.html#T7" target="_self" title="COMPLFLD:th.7">Th7</a></i>;<br/><b>hence </b><a NAME="E4:17_1_2"/>
<font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> 
 <b>by </b><i><a class="txt" href="complfld.html#E2:17"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="complfld.html#E2:17_1_2"><i><font color="Green" title="E11">A4</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self" title="COMPLFLD:th.9">Th9</a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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