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





<b>thus </b><a NAME="E1:70"/>
( <font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font> implies <font color="Maroon">b</font> <a href="lattices.html#R3" target="_self">[=</a> <font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:70_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font>
 ;<br/>

<font color="Maroon">b</font> = 
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" target="_self">Top</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="txt" href="lattices.html#E1:70_1"><i><font color="Green">E34</font></i></a></i>
;<br/>
<a NAME="E3:70_1"/><b>then </b>
<font color="Maroon">b</font> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:70_1"/>
<font color="Maroon">b</font> <a href="lattices.html#R3" target="_self">[=</a> <font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> 
 <b>by </b><i/>;<br/>


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

<b>thus </b><a NAME="E2:70"/>
( <font color="Maroon">b</font> <a href="lattices.html#R3" target="_self">[=</a> <font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a>  implies <font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:70_2"/>
<font color="Maroon">b</font> <a href="lattices.html#R3" target="_self">[=</a> <font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> 
 ;<br/>

<a NAME="E2:70_2"/><b>then </b>
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font> <a href="lattices.html#R3" target="_self">[=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E3:70_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font> <a href="lattices.html#R3" target="_self">[=</a>  <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:70_2"/>
 <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font> <a href="lattices.html#R3" target="_self">[=</a> <font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:70_2"/>
<font color="Maroon">b</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#D8" target="_self">Def8</a></i>;<br/>


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


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