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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> 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="E1:129"/>
( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> or  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>

<a NAME="E2:129"/><b>then </b>
(  ex <font color="Olive" title="b1">x</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Olive" title="b1">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> ) or  ex <font color="Olive" title="b1">x</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Olive" title="b1">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Maroon" title="c2">X</font> ) )
 
<b>by </b><i><a class="ref" href="pboole.html#T11" target="_self" title="PBOOLE:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E3:129"/>
contradiction
 <b>by </b><i><a class="ref" href="pboole.html#T136" target="_self" title="PBOOLE:th.136">Th136</a></i>;<br/>


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