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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> ] <b>means </b> ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,$1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>;<br/>
<b>let </b><font color="Maroon" title="c2">X1</font>, <font color="Maroon" title="c3">X2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3_2_2"/><i><font color="Green" title="E2">A15</font></i>: 
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">y</font>] )
 <b>and </b><br/><a NAME="E2:3_2_2"/><i><font color="Green" title="E3">A16</font></i>: 
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">y</font>] )
 ;<br/>

<b>thus </b><a NAME="E3:3_2_2"/>
<font color="Maroon" title="c2">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X2</font>
 <b>from </b><i><a class="ref" href="xboole_0.html#S2" title="XBOOLE_0:sch.2">XBOOLE_0:sch 2</a>(<a class="txt" href="funct_5.html#E1:3_2_2"><i><font color="Green" title="E2">A15</font></i></a>, <a class="txt" href="funct_5.html#E2:3_2_2"><i><font color="Green" title="E3">A16</font></i></a>);</i><br/>


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