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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">Y</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">Z</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">X</font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>







<b>assume </b><a NAME="E1:145"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">x</font> being   <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font> holds <br/> ( <font color="Olive">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Y</font> &amp; <font color="Olive">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Z</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="145_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:145_1_1"/>
<font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E2:145_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Z</font> )
 <b>by </b><i><a class="ref" href="pboole.html#T24" target="_self">Th24</a></i>;<br/><b>hence </b><a NAME="E3:145_1_1"/>
<font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:145_1"/>
<font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E3:145_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">Z</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:145_1"/>
<font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pboole.html#T24" target="_self">Th24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:145"/>
<font color="Maroon">X</font> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="ref" href="pboole.html#T22" target="_self">Th22</a></i>;<br/>


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