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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NM1" title="PBOOLE:NM.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#K3" title="PBOOLE:func.3">(/\)</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> <font color="Olive" title="b3">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Olive" title="b3">Z</font></span>)</span></span><br/><span class="kw">let </span><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#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</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> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span></span><br/>







<a NAME="E1:74"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T56" target="_self" onmouseover="rs('pboole/T56')" onmouseout="rh()">Th56</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</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"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <font color="Maroon" title="c3">Y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T62" target="_self" onmouseover="rs('pboole/T62')" onmouseout="rh()">Th62</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <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="c4">Z</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c3">Y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T68" target="_self" onmouseover="rs('pboole/T68')" onmouseout="rh()">Th68</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</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="c4">Z</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c3">Y</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T73" target="_self" onmouseover="rs('pboole/T73')" onmouseout="rh()">Th73</a></span>
<br/>.= 
<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="c4">Z</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c2">X</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="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Z</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c3">Y</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T64" target="_self" onmouseover="rs('pboole/T64')" onmouseout="rh()">Th64</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pboole.html#K1" title="PBOOLE:func.1">EmptyMS</a> <font color="Maroon" title="c1">I</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="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Z</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c3">Y</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="pboole.html#T52" target="_self" onmouseover="rs('pboole/T52')" onmouseout="rh()">Th52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T22" target="_self" onmouseover="rs('pboole/T22')" onmouseout="rh()">Th22</a>, <a class="ref" href="pboole.html#T43" target="_self" onmouseover="rs('pboole/T43')" onmouseout="rh()">Th43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</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="c4">Z</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T67" target="_self" onmouseover="rs('pboole/T67')" onmouseout="rh()">Th67</a></span>
<br/>.= 
<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="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <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="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="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T32" target="_self" onmouseover="rs('pboole/T32')" onmouseout="rh()">Th32</a></span>
<br/>.= 
<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="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <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="c4">Z</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <span class="p1">(<span class="default"><a href="pboole.html#K1" title="PBOOLE:func.1">EmptyMS</a> <font color="Maroon" title="c1">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T63" target="_self" onmouseover="rs('pboole/T63')" onmouseout="rh()">Th63</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T22" target="_self" onmouseover="rs('pboole/T22')" onmouseout="rh()">Th22</a>, <a class="ref" href="pboole.html#T43" target="_self" onmouseover="rs('pboole/T43')" onmouseout="rh()">Th43</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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