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<b>let </b><font color="Maroon">L1</font> be  <a href="lattices.html#V3">strict</a> <a href="lattices.html#NM1">Lattice</a>, <font color="Maroon">L2</font> be  <a href="lattices.html#V3">strict</a> <a href="lattices.html#NM1">Lattice</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:23_1_2"/><i><font color="Green">E69</font></i>: 
for <font color="Olive">R</font> being  <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>  st <font color="Olive">R</font> <a href="hidden.html#R1">=</a>  <a href="filter_0.html#K10">equivalence_wrt</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">L1</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> <font color="Olive">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">R</font></span>)</span> #)
 <b>and </b><br/><a NAME="E2:23_1_2"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">R</font> being  <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>  st <font color="Olive">R</font> <a href="hidden.html#R1">=</a>  <a href="filter_0.html#K10">equivalence_wrt</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">L2</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> <font color="Olive">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">R</font></span>)</span> #)
 ;<br/>

<b>reconsider </b><font color="Maroon">I</font> = <font color="Maroon">L</font> as   <a href="filter_0.html#NM2">I_Lattice</a> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">FI</font> = <font color="Maroon">F</font> as    <a href="filter_0.html#M1">Filter</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">o1</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>), <font color="Maroon">o2</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</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/>
<b>thus </b><font color="Maroon">L1</font> = 
 <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">o1</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">o2</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/>.= 
<font color="Maroon">L2</font>
<b>by </b><i/>
;<br/>


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