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<b>thus </b><a NAME="E1:4_2_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  implies  ex <font color="Olive">IT</font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">IT</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E2:4_2_1"/><i><font color="Green">E22</font></i>: 
not <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> 
 ;<br/>

<a NAME="E3:4_2_1"/>
<font color="Maroon">z</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/>
<a NAME="E4:4_2_1"/><b>then </b>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> 2,<a href="numbers.html#K1">REAL</a> </span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="funct_2.html#K1">Funcs</a> 2,<a href="numbers.html#K1">REAL</a>  : <font color="Olive">x</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 0 </span>}</span> 
 
<b>by </b><i>, , <a class="ref" href="numbers.html#D2">NUMBERS:def 2</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">z</font> as   <a href="funct_2.html#NM1">Function</a> of 2, <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="funct_2.html#T121">FUNCT_2:121</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
;<br/>

<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E6:4_2_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 )
 ;<br/>


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