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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b>for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a<sub>2</sub></font> iff ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a<sub>1</sub></font>,<font color="Olive">e</font>] ) );<br/>
<div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:8_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</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">i</font>,<font color="Maroon">a<sub>1</sub></font>];<br/><a NAME="E2:8_1_1"/>
 ex <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>  st <br/>for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Olive">u</font> iff ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">e</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i><b>hence </b><a NAME="E3:8_1_1"/>
 ex <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">i</font>,<font color="Olive">u</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:8_1"/><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E4:8_1"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>]
 <b>from </b><i><a class="ref" href="zfrefle1.html#S1">ZFREFLE1:sch 1</a>();<br/></i>
<a NAME="E5:8_1"/>
<font color="Maroon">f</font> is    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:8_1"/>
 ex <font color="Olive">X</font> being   <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> iff ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Olive">e</font>] ) )
 <b>by </b><i/>;<br/>


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