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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">P<sub>2</sub></font>[<font color="Maroon">a<sub>1</sub></font>] &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() );<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a<sub>1</sub></font>] &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() );<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">F<sub>4</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">C</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">v'</font>) where <font color="Olive">v'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">v'</font>] </span>}</span> ;<br/>
<a NAME="E1:12_1"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds <br/> ( <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">v</font>] iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">v</font>] )
 
<b>by </b><i/>;<br/>
<a NAME="E2:12_1"/><i><font color="Green">E31</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">v'</font>) where <font color="Olive">v'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">v'</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">v'</font>) where <font color="Olive">v'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">v'</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S3" target="_self">FRAENKEL:sch 3</a>();<br/></i>
<a NAME="E3:12_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">v</font>] holds <br/><font color="Maroon">H<sub>2</sub></font>(<font color="Olive">v</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">v</font>)
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:12_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">u'</font>) where <font color="Olive">u'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">u'</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">v'</font>) where <font color="Olive">v'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">v'</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S6" target="_self">FRAENKEL:sch 6</a>();<br/></i>
<b>hence </b><a NAME="E5:12_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="funct_2.html#K3">.</a> <font color="Olive">u'</font></span>)</span> where <font color="Olive">u'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">u'</font>] &amp; <font color="Olive">u'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() ) </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="funct_2.html#K3">.</a> <font color="Olive">v'</font></span>)</span> where <font color="Olive">v'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : ( <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">v'</font>] &amp; <font color="Olive">v'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() ) </span>}</span> 
 <b>by </b><i/>;<br/>


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