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<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green">E26</font></i>: 
not <font color="Maroon">I</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>given </b><font color="Maroon">X</font> being    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font><b> such that </b><a NAME="E2:2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">X</font> is <a href="relat_1.html#V3">empty-yielding</a>
 <b>and </b><br/><a NAME="E3:2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">X</font> is <a href="relat_1.html#V2">non-empty</a>
 ;<br/>

<b>consider </b><font color="Maroon">i</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E6:2"/>
( <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">X</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="pboole.html#D15">PBOOLE:def 15</a>, <a class="ref" href="pboole.html#D16">PBOOLE:def 16</a></i>;<br/>
<b>hence </b><a NAME="E7:2"/>
contradiction
 ;<br/>


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