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<b>let </b><font color="Maroon">I</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">i</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="pralg_1.html#V2">1-sorted-yielding</a> <a href="pencil_1.html#V14">non-Trivial-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>





<a NAME="E1:2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E2:2"/><b>then </b>
<font color="Maroon">A</font> <a href="pralg_1.html#K10">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<b>hence </b><a NAME="E3:2"/>
not <font color="Maroon">A</font> <a href="pralg_1.html#K10">.</a> <font color="Maroon">i</font> is <a href="realset2.html#V3">trivial</a>
 <b>by </b><i><a class="ref" href="pencil_1.html#D17">PENCIL_1:def 17</a></i>;<br/>


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