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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="margrel1.html#K6">BOOLEAN</a>  st <br/>( <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  );<br/>
<b>consider </b><font color="Maroon">IT</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:116_1_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:116_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E31"><i><font color="Green">Lemma94</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">IT</font> = <font color="Maroon">IT</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<b>thus </b><a NAME="E5:116_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp;  ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="margrel1.html#K6">BOOLEAN</a>  st <br/>( <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) ) )
 <b>by </b><i><a class="txt" href="modelc_1.html#E31"><i><font color="Green">Lemma94</font></i></a></i>;<br/>


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