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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">X</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>





<b>assume </b><a NAME="E1:125"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D14" target="_self">PBOOLE:def 14</a><br/>

<b>assume </b><a NAME="E2:125"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x</font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D4" target="_self">PBOOLE:def 4</a><br/>

<b>assume </b><a NAME="E3:125"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<a NAME="E4:125"/><b>then </b>
( <font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T15" target="_self">Th15</a>, <a class="ref" href="pboole.html#T16" target="_self">Th16</a>, , </i>;<br/>
<b>hence </b><a NAME="E5:125"/>
<font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>


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