<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="pboole.html#K5" title="PBOOLE:func.5">\+\</a> <font color="Olive" title="b2">Y</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Olive" title="b3">Z</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b3">Z</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b3">Z</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font>, <font color="Maroon" title="c4">Z</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K5" title="PBOOLE:func.5">\+\</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c4">Z</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Z</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Z</font></span>)</span></span>)</span></span><br/>







<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K5" title="PBOOLE:func.5">\+\</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c4">Z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T78" target="_self" title="PBOOLE:th.78">Th78</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Z</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T79" target="_self" title="PBOOLE:th.79">Th79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Z</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T79" target="_self" title="PBOOLE:th.79">Th79</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
