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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">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>set </b><font color="Maroon">R</font> =  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font>;<br/>
<b>reconsider </b><font color="Maroon">jj</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">I</font>), <font color="Maroon">mm</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">I</font>) as   <a href="filter_1.html#NM4">BinOp</a> of  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font> <b>by </b><i>, </i>;<br/>
<a NAME="E2:25"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">i</font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<font color="Maroon">i</font> &amp; <font color="Maroon">j</font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<font color="Maroon">j</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K3">"\/"</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="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<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/>;<br/>
<a NAME="E3:25"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">I</font> <a href="filter_1.html#K4" target="_self">/\/</a> <font color="Maroon">FI</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">jj</font> <a href="filter_1.html#K3" target="_self">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">mm</font> <a href="filter_1.html#K3" target="_self">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span></span>)</span> #)
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:25"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">j</font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E5:25"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</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="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">FI</font>
 <b>by </b><i>, , </i>;<br/>


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