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<b>let </b><font color="Maroon">I</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">X</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<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>assume </b><a NAME="E1:133"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Y</font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">I</font>
 ;<br/>

<b>assume </b><a NAME="E2:133"/>
<font color="Maroon">X</font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">Y</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font><b> such that </b><br/><a NAME="E4:133"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">x</font> <a href="pboole.html#R3" target="_self">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="pboole.html#R3" target="_self">in</a> <font color="Maroon">Y</font> )
 <b>by </b><i/>;<br/>
<a NAME="E5:133"/>
<font color="Maroon">x</font> <a href="pboole.html#R3" target="_self">in</a> <font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18" target="_self">Th18</a>, </i>;<br/>
<b>hence </b><a NAME="E6:133"/>
contradiction
 <b>by </b><i><a class="ref" href="pboole.html#T17" target="_self">Th17</a>, <a class="ref" href="pboole.html#T15" target="_self">Th15</a></i>;<br/>


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