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<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>, <font color="Maroon">B</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>



<a NAME="E1:15"/><i><font color="Green">E25</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E2:15"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="yellow20.html#K1" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">I</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">AB</font> =  <a href="yellow20.html#K1" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> as    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:15"/>
<font color="Maroon">I</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
;<br/>
<a NAME="E5:15"/><b>then </b>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/><font color="Maroon">AB</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:15"/>
 <a href="yellow20.html#K1" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="pboole.html#K3">/\</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="pboole.html#D8">PBOOLE:def 8</a></i>;<br/>


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