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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">FI</font> be    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">i2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">j1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">j2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/>











<b>assume </b><a NAME="E1:80"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">i1</font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">j1</font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">j2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> )
 ;<br/>

<a NAME="E2:80"/>
( <font color="Maroon">i1</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">i2</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">j1</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">j2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">j2</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> )
 
<b>by </b><i>, <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>
<a NAME="E3:80"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">j2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">i1</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">j1</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">i2</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <font color="Maroon">j2</font> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:80"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:80"/>
( <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j1</font></span>)</span> <a href="filter_0.html#K9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">i2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> )
 <b>by </b><i><a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>


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