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<div class="add">

<b>consider </b><font color="Maroon">c<sub>1</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:99_1"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a>  &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:99_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="membered.html#V1" target="_self">complex-membered</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D1" target="_self">MEMBERED:def 1</a><br/>

<b>assume </b><a NAME="E1:99_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:99_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i><a class="txt" href="membered.html#E2:99_1"><i><font color="Green">E22</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:99_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="xcmplx_0.html#V1">complex</a>
 <b>by </b><i><a class="ref" href="xcmplx_0.html#D2">XCMPLX_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="membered.html#V1" target="_self">complex-membered</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E5:99_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <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>hence </b><a NAME="E6:99_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>] )
 <b>by </b><i><a class="txt" href="membered.html#E2:99_1"><i><font color="Green">E22</font></i></a></i>;<br/>


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