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<b>let </b><font color="Maroon">A1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">A2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7_1_2"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> iff  ex <font color="Olive">j</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> &amp; <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> ) )
 <b>and </b><br/><a NAME="E2:7_1_2"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A2</font> iff  ex <font color="Olive">j</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> &amp; <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> ) )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">j</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> &amp; <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> );<br/>
<a NAME="E3:7_1_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 
<b>by </b><i/>;<br/>
<a NAME="E4:7_1_2"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 
<b>by </b><i/>;<br/>
<a NAME="E5:7_1_2"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font>
 
<b>from </b><i><a class="ref" href="xboole_0.html#S2">XBOOLE_0:sch 2</a>(, );<br/></i>
<b>hence </b><a NAME="E6:7_1_2"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font>
 ;<br/>


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