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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>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a><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="E1:41"/>
( <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font> <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="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font> <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">k</font></span>)</span> <a href="lattices.html#K3">"\/"</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> &amp; <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#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#K3">"\/"</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> )
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a></i>;<br/>
<a NAME="E2:41"/><b>then </b>
( <font color="Maroon">j</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="filter_0.html#K4" target="_self">=&gt;</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="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span></span>)</span> &amp; <font color="Maroon">k</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="filter_0.html#K4" target="_self">=&gt;</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="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E3:41"/><b>then </b>
<font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="filter_0.html#K4" target="_self">=&gt;</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="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:41"/><b>then </b>
( <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#R3">[=</a> <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" target="_self">=&gt;</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="lattices.html#K3">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> &amp; <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" target="_self">=&gt;</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="lattices.html#K3">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span></span>)</span></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="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T1" target="_self">Th1</a>, <a class="ref" href="lattices.html#T27">LATTICES:27</a></i>;<br/>
<a NAME="E5:41"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</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="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>
<a NAME="E6:41"/>
( <font color="Maroon">j</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">k</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j</font> &amp; <font color="Maroon">k</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a></i>;<br/>
<a NAME="E7:41"/><b>then </b>
( <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="lattices.html#T27">LATTICES:27</a></i>;<br/>
<a NAME="E8:41"/><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#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">k</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:41"/>
<font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</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="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K4">"/\"</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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