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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_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> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Olive" title="b1">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b2">Y</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Olive" title="b1">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  &amp; <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> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  holds <br/>( <font color="Olive" title="b1">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Olive" title="b1">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  &amp; <font color="Olive" title="b2">Y</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Olive" title="b2">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</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"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  &amp; <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 href="lattices.html#K7" title="LATTICES:func.7">`</a>  implies ( <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  &amp; <font color="Maroon" title="c3">Y</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  ) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:56"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font>
 <span class="kw">and </span><br/><a NAME="E2:56"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c3">Y</font> <a href="boolealg.html#R4" title="BOOLEALG:pred.4">misses</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 <span class="kw">and </span><br/><a NAME="E3:56"/><span class="lab"><font color="Green" title="E22">A3</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 href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 ; <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#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  &amp; <font color="Maroon" title="c3">Y</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  )</span><br/>

<a NAME="E4:56"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<font color="Maroon" title="c3">Y</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#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a>  <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="txt" href="#E2:56"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="boolealg.html#D4" target="_self" title="BOOLEALG:def.4">Def4</a></span>;<br/>
<a NAME="E5:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font></span>)</span> <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#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#T11" title="LATTICES:th.11">LATTICES:11</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> = 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#T21" title="LATTICES:th.21">LATTICES:21</a></span>
<br/>.= 
<font color="Maroon" title="c2">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T14" title="LATTICES:th.14">LATTICES:14</a></span>
;<br/>
<a NAME="E7:56"/><span class="kw">then </span>
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T17" title="LATTICES:th.17">LATTICES:17</a></span>;<br/>
<a NAME="E8:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>;<br/>
<a NAME="E9:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A5</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E10:56"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a>  <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="txt" href="#E3:56"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="boolealg.html#D4" target="_self" title="BOOLEALG:def.4">Def4</a></span>;<br/>
<a NAME="E11:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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="c3">Y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#T11" title="LATTICES:th.11">LATTICES:11</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> = 
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#T21" title="LATTICES:th.21">LATTICES:21</a></span>
<br/>.= 
<font color="Maroon" title="c3">Y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T14" title="LATTICES:th.14">LATTICES:14</a></span>
;<br/>
<a NAME="E13:56"/><span class="kw">then </span>
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T17" title="LATTICES:th.17">LATTICES:17</a></span>;<br/>
<a NAME="E14:56"/><span class="kw">then </span>
<span class="p1">(<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#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>;<br/>
<a NAME="E15:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E16:56"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font></span>)</span> <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="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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="txt" href="#E4:56"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="lattices.html#T11" title="LATTICES:th.11">LATTICES:11</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <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="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#T21" title="LATTICES:th.21">LATTICES:21</a></span>
<br/>.= 
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T14" title="LATTICES:th.14">LATTICES:14</a></span>
;<br/>
<a NAME="E18:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T17" title="LATTICES:th.17">LATTICES:17</a></span>;<br/>
<a NAME="E19:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <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#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>;<br/>
<a NAME="E20:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <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#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E21:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E22:56"/><span class="kw">then </span>
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E23:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A8</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E24:56"/>
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T5" title="LATTICES:th.5">LATTICES:5</a></span>;<br/>
<a NAME="E25:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A9</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:56"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="ref" href="lattices.html#T7" title="LATTICES:th.7">LATTICES:7</a></span>;<br/>
<a NAME="E26:56"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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="txt" href="#E10:56"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="lattices.html#T11" title="LATTICES:th.11">LATTICES:11</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <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#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#T21" title="LATTICES:th.21">LATTICES:21</a></span>
<br/>.= 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T14" title="LATTICES:th.14">LATTICES:14</a></span>
;<br/>
<a NAME="E28:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T17" title="LATTICES:th.17">LATTICES:17</a></span>;<br/>
<a NAME="E29:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>;<br/>
<a NAME="E30:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E31:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E32:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E33:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A10</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E34:56"/>
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T5" title="LATTICES:th.5">LATTICES:5</a></span>;<br/>
<a NAME="E35:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A11</font></span>: 
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:56"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="ref" href="lattices.html#T7" title="LATTICES:th.7">LATTICES:7</a></span>;<br/>
<a NAME="E36:56"/>
<font color="Maroon" title="c2">X</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T5" title="LATTICES:th.5">LATTICES:5</a></span>;<br/>
<a NAME="E37:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A12</font></span>: 
<font color="Maroon" title="c2">X</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:56"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="lattices.html#T7" title="LATTICES:th.7">LATTICES:7</a></span>;<br/>
<a NAME="E38:56"/>
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T5" title="LATTICES:th.5">LATTICES:5</a></span>;<br/>
<a NAME="E39:56"/><span class="kw">then </span>
<font color="Maroon" title="c3">Y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:56"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="lattices.html#T7" title="LATTICES:th.7">LATTICES:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E40:56"/>
( <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  &amp; <font color="Maroon" title="c3">Y</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a> <font color="Maroon" title="c3">Y</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:56"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="txt" href="#E25:56"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="txt" href="#E37:56"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="ref" href="boolealg.html#D3" target="_self" title="BOOLEALG:def.3">Def3</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/>


</div>
