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<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font>, <font color="Maroon" title="c4">k</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c5">FI</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">I</font>;<br/>









<b>assume </b><a NAME="E1:82"/><i><font color="Green" title="E58">A1</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c3">j</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> )
 ;<br/>

<a NAME="E2:82"/>
( <font color="Maroon" title="c2">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c3">j</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c3">j</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c4">k</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> )
 
<b>by </b><i><a class="txt" href="filter_0.html#E1:82"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="filter_0.html#D1" target="_self" title="FILTER_0:def.1">Def1</a></i>;<br/>
<a NAME="E3:82"/><b>then </b>
( <font color="Maroon" title="c2">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c4">k</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c2">i</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c2">i</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T54" target="_self" title="FILTER_0:th.54">Th54</a></i>;<br/>
<b>hence </b><a NAME="E4:82"/>
<font color="Maroon" title="c2">i</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font>
 <b>by </b><i><a class="ref" href="filter_0.html#D1" target="_self" title="FILTER_0:def.1">Def1</a></i>;<br/>


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