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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">Y</font> being  <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Olive">Y</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Olive">Y</font> );<br/>
<a NAME="E1:7_1_1"/>
 ex <font color="Olive">Z</font> being  <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">X</font> st <br/>for <font color="Olive">x</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">Z</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 
<b>from </b><i><a class="ref" href="subset_1.html#S3">SUBSET_1:sch 3</a>();<br/></i>
<b>hence </b><a NAME="E2:7_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">X</font> st <br/>for <font color="Olive">x</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> iff  ex <font color="Olive">Y</font> being  <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Olive">Y</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Olive">Y</font> ) )
 ;<br/>


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