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







<b>assume </b><b>that </b><br/><a NAME="E1:112"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#NR7" target="_self">meets</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E2:112"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">Y</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">Z</font>
 ;<br/>

<b>consider </b><font color="Maroon">i</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:112"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</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="xboole_0.html#NR5" target="_self">meets</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#T8" target="_self">Th8</a>, </i>;<br/>
<b>take </b>
<font color="Maroon">i</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D11" target="_self">PBOOLE:def 11</a><br/>

<a NAME="E5:112"/>
<font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T9" target="_self">Th9</a>, <a class="ref" href="pboole.html#T10" target="_self">Th10</a>, </i>;<br/>
<b>hence </b><a NAME="E6:112"/>
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; not <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Z</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>


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