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

<b>let </b><font color="Maroon">X1</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X1</font>;<br/><b>let </b><font color="Maroon">B1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X1</font>;<br/>





<a NAME="E1:43"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">x1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> holds <br/> ( ( not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> iff <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) iff ( ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) or ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> ) ) )
 
;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>( not <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> iff <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</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">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) or ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> &amp; not <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> ) );<br/>
<a NAME="E2:43"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">X1</font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>   st ( for <font color="Olive">x1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">X1</font> holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x1</font>] iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">x1</font>] ) ) holds <br/><span class="p1">{<span class="default"> <font color="Olive">y1</font> where <font color="Olive">y1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Olive">X1</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y1</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">z1</font> where <font color="Olive">z1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Olive">X1</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">z1</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S6" target="_self">DOMAIN_1:sch 6</a>();<br/></i>
<a NAME="E3:43"/>
<font color="Maroon">A1</font> <a href="subset_1.html#K5">\+\</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">x1</font> where <font color="Olive">x1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> : ( not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> iff <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:43"/>
<font color="Maroon">A1</font> <a href="subset_1.html#K5">\+\</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">x1</font> where <font color="Olive">x1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> : ( ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) or ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> ) ) </span>}</span> 
 <b>by </b><i>, </i>;<br/>


</div>
