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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">M</font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>



<b>assume </b><a NAME="E1:150"/><i><font color="Green">E24</font></i>: 
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E2:150"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:150"/><b>then </b>
 ex <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="pboole.html#T25" target="_self">Th25</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:150"/>
contradiction
 <b>by </b><i><a class="ref" href="pboole.html#T18" target="_self">Th18</a></i>;<br/>


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