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

<b>reconsider </b><font color="Maroon">NE</font> =  <a href="pralg_3.html#K1" target="_self">id</a> <font color="Maroon">X</font> as    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font> ;<br/>
<a NAME="E2:3_1_1"/>
<font color="Maroon">NE</font> is <a href="relat_1.html#V2">non-empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D16">PBOOLE:def 16</a><br/>

<b>assume </b><a NAME="E1:3_1_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:3_1_1_1"/><b>then </b>
<font color="Maroon">NE</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<b>hence </b><a NAME="E3:3_1_1_1"/>
not <font color="Maroon">NE</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, <a class="ref" href="setfam_1.html#D9">SETFAM_1:def 9</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:3_1_1"/>
 <a href="pralg_3.html#K1" target="_self">id</a> <font color="Maroon">X</font> is <a href="relat_1.html#V2">non-empty</a>
 ;<br/>


</div>
