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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">F_Complex</a> ;<br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green">E18</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>2</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">COMPLFLD:def 1</a></i>;<br/>
<a NAME="E3:15"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:15"><i><font color="Green">E18</font></i></a>, <a class="ref" href="complex1.html#T136">COMPLEX1:136</a></i>;<br/>
<a NAME="E4:15"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:15"><i><font color="Green">E18</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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