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<b>let </b><font color="Maroon" title="c1">I</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/>





<b>assume </b><a NAME="E1:130"/><i><font color="Green" title="E71">A1</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font>
 ;<br/>

<b>assume </b><a NAME="E2:130"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><b> such that </b><br/><a NAME="E4:130"/><i><font color="Green" title="E72">A2</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Maroon" title="c3">Y</font> )
 <b>by </b><i><a class="ref" href="pboole.html#T11" target="_self" title="PBOOLE:th.11">Th11</a></i>;<br/>
<a NAME="E5:130"/>
<font color="Maroon" title="c4">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Maroon" title="c2">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="txt" href="pboole.html#E4:130"><i><font color="Green" title="E72">A2</font></i></a>, <a class="ref" href="pboole.html#T8" target="_self" title="PBOOLE:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E6:130"/>
contradiction
 <b>by </b><i><a class="txt" href="pboole.html#E1:130"><i><font color="Green" title="E71">A1</font></i></a>, <a class="ref" href="pboole.html#T136" target="_self" title="PBOOLE:th.136">Th136</a></i>;<br/>


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