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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>( <font color="Maroon">a<sub>1</sub></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="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/>
<a NAME="E1:116_1_2"/>
for <font color="Olive">X1</font>, <font color="Olive">X2</font> being   <a href="hidden.html#M1">set</a>   st ( 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="Olive">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) ) &amp; ( 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="Olive">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) ) holds <br/><font color="Olive">X1</font> <a href="hidden.html#R1">=</a> <font color="Olive">X2</font>
 
<b>from </b><i><a class="ref" href="xboole_0.html#S3">XBOOLE_0:sch 3</a>();<br/></i>
<b>hence </b><a NAME="E2:116_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>  st ( 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="Olive">b<sub>1</sub></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>  ) ) ) ) &amp; ( 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="Olive">b<sub>2</sub></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>  ) ) ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
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