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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <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/>

<i><font color="Green">E10</font></i>:  <a href="complex1.html#K5">0c</a>  = 
the <a href="struct_0.html#U2">Zero</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> 
<b>by </b><i><a class="ref" href="complfld.html#D1" target="_self">Def1</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1" target="_self">F_Complex</a> 

;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</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>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</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="xcmplx_0.html#D2">XCMPLX_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="complex1.html#K12">"</a>  as   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self">Def1</a></i>;<br/>
<font color="Maroon">c<sub>1</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="complfld.html#T6" target="_self">Th6</a></i>
<br/>.= 
 <a href="complex1.html#K6">1r</a> 
<b>by </b><i><a class="txt" href="complfld.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="complfld.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1" target="_self">F_Complex</a> 
<b>by </b><i><a class="txt" href="complfld.html#E5"><i><font color="Green">Lemma3</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E7:12"/>
<font color="Maroon">c<sub>1</sub></font> <a href="vectsp_1.html#K4">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> 
 <b>by </b><i><a class="txt" href="complfld.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>;<br/>


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