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<b>let </b><font color="Maroon">B</font> be   <a href="lattices.html#NM8">B_Lattice</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">B</font>;<br/>





<b>reconsider </b><font color="Maroon">B'</font> = <font color="Maroon">B</font> as   <a href="lattices.html#NM4">0_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">B''</font> = <font color="Maroon">B</font> as   <a href="lattices.html#NM5">1_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">D</font> = <font color="Maroon">B</font> as   <a href="lattices.html#NM2">D_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">c'</font> = <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K7">`</a> </span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">B'</font> ;<br/>
<b>reconsider </b><font color="Maroon">a''</font> = <font color="Maroon">a</font>, <font color="Maroon">b''</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">B''</font> ;<br/>
<b>reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">a</font>, <font color="Maroon">b1</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> ;<br/>
<b>thus </b><a NAME="E7:60"/>
( <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font> implies <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b</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">B</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_1"/>
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:60_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T21">LATTICES:21</a></i>;<br/>
<b>hence </b><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K7">`</a> </span>)</span> = 
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<font color="Maroon">a'</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">B'</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>
<br/>.= 
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="lattices.html#T40">LATTICES:40</a></i>
;<br/><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E8:60"/>
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b</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">B</font>
 ;<br/>

<b>then </b><font color="Maroon">b</font> = 
<font color="Maroon">b'</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c'</font>
<b>by </b><i><a class="ref" href="lattices.html#T39">LATTICES:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a1</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T31">LATTICES:31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b''</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a''</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">B''</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T48">LATTICES:48</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="lattices.html#T43">LATTICES:43</a></i>
;<br/>
<b>hence </b><a NAME="E10:60"/>
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>


</div>
