<?xml version="1.0"?>
<div class="add">

<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>assume </b><a NAME="E1:142"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X</font> is <a href="relat_1.html#V2">non-empty</a>
 ;<br/>

<b>assume </b><a NAME="E2:142"/>
<font color="Maroon">X</font> <a href="pboole.html#R7" target="_self">[=</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E3:142"/><b>then </b>
<font color="Maroon">X</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T22" target="_self">Th22</a>, <a class="ref" href="pboole.html#T21" target="_self">Th21</a></i>;<br/>
<b>hence </b><a NAME="E4:142"/>
<font color="Maroon">Y</font> is <a href="relat_1.html#V2">non-empty</a>
 <b>by </b><i><a class="ref" href="pboole.html#T22" target="_self">Th22</a>, <a class="ref" href="pboole.html#T19" target="_self">Th19</a></i>;<br/>


</div>
