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





<b>assume </b><a NAME="E1:81"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#K3">/\</a> <font color="Maroon">Y</font> <a href="pboole.html#R6">=</a>  <a href="pboole.html#K1">[0]</a> <font color="Maroon">I</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:81_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K3">/\</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="pboole.html#D8">PBOOLE:def 8</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="pboole.html#T5">PBOOLE:5</a></i>
;<br/><a NAME="E3:81_1"/><b>then </b>
<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">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E4:81_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T127">ZFMISC_1:127</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="pboole.html#K10">|]</a></span> <a href="pboole.html#K3">/\</a> <span class="p2"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">Y</font>,<font color="Maroon">X</font></span><a href="pboole.html#K10">|]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="pboole.html#K10">|]</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">Y</font>,<font color="Maroon">X</font></span><a href="pboole.html#K10">|]</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="pboole.html#D8">PBOOLE:def 8</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">Y</font>,<font color="Maroon">X</font></span><a href="pboole.html#K10">|]</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="pboole.html#D21">PBOOLE:def 21</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, <a class="ref" href="pboole.html#D21">PBOOLE:def 21</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pboole.html#K1">[0]</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="pboole.html#T5">PBOOLE:5</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:81"/>
<span class="p1"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="pboole.html#K10">|]</a></span> <a href="pboole.html#K3">/\</a> <span class="p1"><a href="pboole.html#K10">[|</a><span class="default"><font color="Maroon">Y</font>,<font color="Maroon">X</font></span><a href="pboole.html#K10">|]</a></span> <a href="pboole.html#R6">=</a>  <a href="pboole.html#K1">[0]</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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