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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">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>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>assume </b><a NAME="E1:107"/>
<font color="Maroon">X</font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</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="E3:107"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">X</font> &amp; <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/>
<a NAME="E4:107"/>
( <font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">X</font> &amp; <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#T7" target="_self">Th7</a>, </i>;<br/>
<b>hence </b><a NAME="E5:107"/>
( <font color="Maroon">X</font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">X</font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">Z</font> )
 <b>by </b><i/>;<br/>


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