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<span class="kw">reconsider </span><font color="Maroon" title="c3">I</font> = <font color="Maroon" title="c1">L</font> as   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">FI</font> = <font color="Maroon" title="c2">F</font> as   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c3">I</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">j</font> =  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c3">I</font>, <font color="Maroon" title="c6">m</font> =  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c3">I</font> as   <a href="filter_1.html#NM4" title="FILTER_1:NM.4">BinOp</a> of  <a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T13" target="_self" onmouseover="rs('filter_1/T13')" onmouseout="rh()">Th13</a>, <a class="ref" href="filter_1.html#T14" target="_self" onmouseover="rs('filter_1/T14')" onmouseout="rh()">Th14</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">LL</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font></span>)</span></span>)</span> #) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>   <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a>  ;<br/>
<a NAME="E5:21_1_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T4" target="_self" onmouseover="rs('filter_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E6:21_1_1"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T5" target="_self" onmouseover="rs('filter_1/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E7:21_1_1"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T5" target="_self" onmouseover="rs('filter_1/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E8:21_1_1"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T4" target="_self" onmouseover="rs('filter_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E9:21_1_1"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T12" target="_self" onmouseover="rs('filter_1/T12')" onmouseout="rh()">Th12</a>, <a class="ref" href="lattice2.html#T27" onmouseover="rs('lattice2/T27')" onmouseout="rh()">LATTICE2:27</a></span>;<br/>
<a NAME="E10:21_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T12" target="_self" onmouseover="rs('filter_1/T12')" onmouseout="rh()">Th12</a>, <a class="ref" href="lattice2.html#T26" onmouseover="rs('lattice2/T26')" onmouseout="rh()">LATTICE2:26</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">LL</font> = <font color="Maroon" title="c7">LL</font> as   <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21_1_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E6:21_1_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E8:21_1_1"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:21_1_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E9:21_1_1"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="lattice2.html#T11" onmouseover="rs('lattice2/T11')" onmouseout="rh()">LATTICE2:11</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">LL</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K8" title="FILTER_0:func.8">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c8">LL</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span> #)</span><br/>

<span class="kw">thus </span><a NAME="E12:21_1_1"/>
 for <font color="Olive" title="b1">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K8" title="FILTER_0:func.8">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c8">LL</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span> #)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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