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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">A</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>, <font color="Maroon">B</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:50"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Fi</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <b>by </b><i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E3:50"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="msafree.html#K1">||</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 ;<br/>

<a NAME="E4:50"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Fi</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="msafree.html#D1">MSAFREE:def 1</a></i>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E5:50"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> implies <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


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