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<b>thus </b><a NAME="E1:7_1_1"/>
 ex <font color="Olive">R</font> being  <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">S</font> st <br/>for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> holds <br/> ( <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Olive">R</font> iff  ex <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">B</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_1"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>] <b>means </b> ex <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">B</font> );<br/>
<a NAME="E1:7_1_1_1"/>
 ex <font color="Olive">R</font> being  <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">S</font> st <br/>for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> holds <br/> ( <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Olive">R</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">A</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_1"/>
 ex <font color="Olive">R</font> being  <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">S</font> st <br/>for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> holds <br/> ( <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Olive">R</font> iff  ex <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">B</font> ) )
 ;<br/>


</div><b>end;</b></div>


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