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<b>let </b><font color="Maroon">I</font> be   <a href="filter_0.html#NM2">I_Lattice</a>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">k</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/>







<a NAME="E1:27"/>
( <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</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">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">k</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">i</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span></span>)</span> &amp; <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">i</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E2:27"/><b>then </b>
<font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>
<a NAME="E3:27"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>
<a NAME="E4:27"/>
<font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>
<a NAME="E5:27"/><b>then </b>
( <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span> &amp; <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">i</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a>, <a class="ref" href="lattices.html#T27">LATTICES:27</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E6:27"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>
<a NAME="E7:27"/><b>then </b>
<font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>
<b>hence </b><a NAME="E8:27"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>


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