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<b>let </b><font color="Maroon">z2</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> ;<br/><b>let </b><font color="Maroon">z1</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> ;<br/><b>let </b><font color="Maroon">z3</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">z1'</font> = <font color="Maroon">z1</font>, <font color="Maroon">z2'</font> = <font color="Maroon">z2</font>, <font color="Maroon">z3'</font> = <font color="Maroon">z3</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:22"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">z2</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="E3:22"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">z1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font> or <font color="Maroon">z2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font> )
 ;<br/>

<a NAME="E4:22"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">z2'</font> <a href="binop_2.html#K2">"</a> 
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1"/>
( <font color="Maroon">z1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font> or <font color="Maroon">z2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1"><b>suppose </b></a><a NAME="E1:22_1_1"/>
<font color="Maroon">z1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font>
 ;<br/><div class="add"><a NAME="E2:22_1_1"/><b>then </b>
<font color="Maroon">z1'</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">z2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3'</font>
 <b>by </b><i/>;<br/><a NAME="E3:22_1_1"/><b>then </b>
<font color="Maroon">z1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3'</font> <a href="binop_2.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">z2'</font> <a href="binop_2.html#K2">"</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T204">XCMPLX_1:204</a></i>;<br/><b>hence </b><a NAME="E4:22_1_1"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a> </span>)</span> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">z3</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2"><b>suppose </b></a><a NAME="E1:22_1_2"/>
<font color="Maroon">z2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font>
 ;<br/><div class="add"><a NAME="E2:22_1_2"/><b>then </b>
<font color="Maroon">z2'</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">z1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3'</font>
 <b>by </b><i/>;<br/><a NAME="E3:22_1_2"/><b>then </b>
<font color="Maroon">z1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3'</font> <a href="binop_2.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">z2'</font> <a href="binop_2.html#K2">"</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T204">XCMPLX_1:204</a></i>;<br/><b>hence </b><a NAME="E4:22_1_2"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z3</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a> </span>)</span> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">z3</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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