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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a>; <a class="txt" 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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Olive" title="b2">Y</font> holds <br/><font color="Olive" title="b3">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Olive" title="b3">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">Y</font></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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c3">Y</font> implies <font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">Y</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:22"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c3">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">Y</font></span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">Y</font></span>)</span> = 
<font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">Z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">Z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="boolealg.html#D4" target="_self" title="BOOLEALG:def.4">Def4</a></span>
<br/>.= 
<font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T15" title="LATTICES:th.15">LATTICES:15</a></span>
<br/>.= 
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T15" title="LATTICES:th.15">LATTICES:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:22"/>
<font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c4">Z</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="boolealg.html#D4" target="_self" title="BOOLEALG:def.4">Def4</a></span>; <a class="txt" 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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