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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>( $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[$1,$2] );<br/>
<a NAME="E1:23_1"/><i><font color="Green" title="E4">A1</font></i>: 
for <font color="Olive" title="b1">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive" title="b2">t</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>] iff ( <font color="Olive" title="b2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>] ) )
 
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<b>thus </b><a NAME="E2:23_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>) where <font color="Olive" title="b1">s</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">t</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>] </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s'</font>,<font color="Maroon">F<sub>4</sub></font>()) where <font color="Olive" title="b1">s'</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">s'</font>,<font color="Maroon">F<sub>4</sub></font>()] </span>}</span> 
 <b>from </b><i><a class="ref" href="fraenkel.html#S19" target="_self" title="FRAENKEL:sch.19">FRAENKEL:sch 19</a>(<a class="txt" href="fraenkel.html#E1:23_1"><i><font color="Green" title="E4">A1</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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