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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:132"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R4" target="_self">overlaps</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">c<sub>1</sub></font> or  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">c<sub>1</sub></font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:132"/><b>then </b>
( ex <font color="Olive">b<sub>1</sub></font> being   <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R3" target="_self">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R3" target="_self">in</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">c<sub>1</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being   <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R3" target="_self">in</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R3" target="_self">in</a> <font color="Maroon">c<sub>2</sub></font> ) )
 
<b>by </b><i><a class="ref" href="pboole.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E3:132"/>
contradiction
 <b>by </b><i><a class="ref" href="pboole.html#T136" target="_self">Th136</a></i>;<br/>


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