<?xml version="1.0"?>
<div class="add">

<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#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>($1);<br/>
<div><i><font color="Green" title="E3">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c1">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>consider </b><font color="Maroon" title="c2">fe</font> being    <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" title="c1">e</font>);<br/><b>assume </b><a NAME="E2:4_1_1"/>
<font color="Maroon" title="c1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/><a NAME="E3:4_1_1"/><b>then </b><i><font color="Green" title="E4">A3</font></i>: 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c1">e</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="pboole.html#E1:4"><i><font color="Green" title="E2">A1</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c3">fe</font> = <font color="Maroon" title="c2">fe</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><b>take </b><font color="Maroon" title="c4">fe</font> = <font color="Maroon" title="c3">fe</font>;<br/><b>thus </b><a NAME="E5:4_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">e</font>,<font color="Maroon" title="c4">fe</font>]
 <b>by </b><i><a class="txt" href="pboole.html#E3:4_1_1"><i><font color="Green" title="E4">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:4_1"/><i><font color="Green" title="E4">A4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E4:4_1"/><i><font color="Green" title="E5">A5</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font>]
 <b>from </b><i><a class="ref" href="classes1.html#S1" title="CLASSES1:sch.1">CLASSES1:sch 1</a>(<a class="txt" href="pboole.html#E1:4_1"><i><font color="Green" title="E3">A2</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c2">f</font> = <font color="Maroon" title="c1">f</font> as    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i><a class="txt" href="pboole.html#E3:4_1"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="pboole.html#D3" target="_self" title="PBOOLE:def.3">Def3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">f</font>
;<br/>

<b>thus </b><a NAME="E6:4_1"/>
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">e</font>)
 <b>by </b><i><a class="txt" href="pboole.html#E4:4_1"><i><font color="Green" title="E5">A5</font></i></a></i>;<br/>


</div>
