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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/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_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="E1:72_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K4" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">Z</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<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="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">Z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<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="subset_1.html#K6">\</a> <span class="p1">(<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> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">Z</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<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> <a href="subset_1.html#K6">\</a> <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>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<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> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">Z</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T52">XBOOLE_1:52</a></i>
<br/>.= 
<span class="p1">(<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> <a href="subset_1.html#K6">\</a> <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>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<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="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<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="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">Y</font></span>)</span> <a href="pboole.html#K2" target="_self">\/</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">Z</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:72"/>
<font color="Maroon">X</font> <a href="pboole.html#K4" target="_self">\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">Z</font></span>)</span> <a href="pboole.html#R6" target="_self">=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">Y</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">Z</font></span>)</span>
 <b>by </b><i/>;<br/>


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