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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="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">E</font> be    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K2" target="_self">Bool</a> <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">T</font> be    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K2" target="_self">Bool</a> <font color="Maroon">M</font>;<br/>







<a NAME="E1:20"/>
<font color="Maroon">E</font> <a href="pboole.html#K5">\+\</a> <font color="Maroon">T</font> is    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1"/>
( <font color="Maroon">E</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">M</font> &amp; <font color="Maroon">T</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E2:20_1"/><b>then </b>
( <font color="Maroon">E</font> <a href="pboole.html#K4">\</a> <font color="Maroon">T</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">M</font> &amp; <font color="Maroon">T</font> <a href="pboole.html#K4">\</a> <font color="Maroon">E</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="mboolean.html#T16">MBOOLEAN:16</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon">E</font> <a href="pboole.html#K5">\+\</a> <font color="Maroon">T</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="ref" href="pboole.html#T99">PBOOLE:99</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:20"/>
<font color="Maroon">E</font> <a href="pboole.html#K5">\+\</a> <font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="closure2.html#K2" target="_self">Bool</a> <font color="Maroon">M</font>
 <b>by </b><i/>;<br/>


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