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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="filter_0.html#K10">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">b<sub>1</sub></font></span>)</span> #)
 <b>and </b><br/><a NAME="E2:23_1_2"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="filter_0.html#K10">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></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">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">b<sub>1</sub></font></span>)</span> #)
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="filter_0.html#NM2">I_Lattice</a> <b>by </b><i><a class="txt" href="filter_1.html#E1:23"><i><font color="Green">E15</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">c<sub>5</sub></font> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>6</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>), <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) as   <a href="filter_1.html#NM4">BinOp</a> of  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>6</sub></font> <b>by </b><i><a class="ref" href="filter_1.html#T13" target="_self">Th13</a>, <a class="ref" href="filter_1.html#T14" target="_self">Th14</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>3</sub></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">c<sub>6</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></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">c<sub>6</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></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">c<sub>6</sub></font></span>)</span></span>)</span> #)
<b>by </b><i><a class="txt" href="filter_1.html#E1:23_1_2"><i><font color="Green">E16</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="filter_1.html#E2:23_1_2"><i><font color="Green">E17</font></i></a></i>
;<br/>


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