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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/>

<b>assume </b><a NAME="E1:34"/>
<font color="Maroon">L</font> is   <a href="lattices.html#NM8">B_Lattice</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">S</font> = <font color="Maroon">L</font> as   <a href="lattices.html#NM8">B_Lattice</a> ;<br/>
<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>set </b><font color="Maroon">r</font> = <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>;<br/>
<b>reconsider </b><font color="Maroon">K</font> = <font color="Maroon">S</font> as   <a href="lattices.html#NM4">0_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">J</font> = <font color="Maroon">S</font> as   <a href="lattices.html#NM5">1_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font>, <font color="Maroon">q'</font> = <font color="Maroon">q</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> ;<br/>
<b>reconsider </b><font color="Maroon">p''</font> = <font color="Maroon">p</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E7:34"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">p''</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">p''</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp; <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">K</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q'</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q'</font> &amp; <font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T39">LATTICES:39</a>, <a class="ref" href="lattices.html#T47">LATTICES:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">K</font> = <font color="Maroon">S</font> as   <a href="lattices.html#NM2">D_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font>, <font color="Maroon">q'</font> = <font color="Maroon">q</font>, <font color="Maroon">r'</font> = <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> ;<br/>
<a NAME="E10:34"/>
<font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q'</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>;<br/>
<b>hence </b><a NAME="E11:34"/>
<font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#T23">LATTICES:23</a></i>;<br/>

<b>let </b><font color="Maroon">r1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<b>reconsider </b><font color="Maroon">r1'</font> = <font color="Maroon">r1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> ;<br/>
<b>reconsider </b><font color="Maroon">pp</font> = <font color="Maroon">p</font>, <font color="Maroon">r''</font> = <font color="Maroon">r1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">J</font> ;<br/>
<b>assume </b><a NAME="E14:34"/>
<font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r1</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E15:34"/><b>then </b><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r1</font></span>)</span> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
 
<b>by </b><i/>;<br/>
<a NAME="E16:34"/>
( <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r1'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p'</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r1'</font></span>)</span> &amp; <font color="Maroon">r1</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">r1</font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p''</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p''</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font> &amp; <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">J</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">pp</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r''</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">pp</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r''</font> &amp; <font color="Maroon">r1</font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r1</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a>, <a class="ref" href="lattices.html#T31">LATTICES:31</a>, <a class="ref" href="lattices.html#T43">LATTICES:43</a>, <a class="ref" href="lattices.html#T48">LATTICES:48</a></i>;<br/>
<b>hence </b><a NAME="E17:34"/>
<font color="Maroon">r1</font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="filter_0.html#T1" target="_self">Th1</a>, <a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>


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