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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">Z</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">V</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</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>;<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="E1:119"/>
<font color="Maroon">Z</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">V</font> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">X</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:119"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">X</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">Z</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">V</font> &amp; <font color="Maroon">Y</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">Z</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">V</font> &amp; <font color="Maroon">Z</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">X</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">V</font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">X</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">Y</font> )
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E3:119"/>
( <font color="Maroon">X</font> <a href="pboole.html#R5" target="_self">misses</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">Y</font> <a href="pboole.html#R5" target="_self">misses</a> <font color="Maroon">V</font> )
 ;<br/>

<a NAME="E4:119"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">I</font> &amp; <font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">V</font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">I</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T9" target="_self">Th9</a></i>;<br/>
<b>thus </b><font color="Maroon">X</font> = 
<font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Z</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font></span>)</span> <a href="pboole.html#K2" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">Y</font></span>)</span> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">V</font>
<b>by </b><i><a class="ref" href="pboole.html#T11" target="_self">Th11</a>, <a class="ref" href="pboole.html#D3" target="_self">Def3</a></i>
<br/>.= 
<font color="Maroon">V</font>
<b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a>, </i>
;<br/>

<b>thus </b><font color="Maroon">Y</font> = 
<font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Z</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font></span>)</span> <a href="pboole.html#K2" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">Y</font></span>)</span> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font>
<b>by </b><i><a class="ref" href="pboole.html#T11" target="_self">Th11</a>, <a class="ref" href="pboole.html#D3" target="_self">Def3</a></i>
<br/>.= 
<font color="Maroon">Z</font>
<b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a>, </i>
;<br/>


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