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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L2</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L2</font> #) implies for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">L1</font> holds <br/><font color="Olive" title="b1">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c2">L2</font> )</span><br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E11">A1</font></i>: 
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L2</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L2</font> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">L1</font> holds <br/><font color="Olive" title="b1">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c2">L2</font></span><br/>

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">L1</font> implies <font color="Maroon" title="c3">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c2">L2</font> )</span><br/>

<b>assume </b><a NAME="E2:20"/>
<font color="Maroon" title="c3">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">L1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c2">L2</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c3">x</font> as    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">L1</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) iff <font color="Maroon" title="c5">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> )</span><br/><b>reconsider </b><font color="Maroon" title="c7">a'</font> = <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c8">b'</font> = <font color="Maroon" title="c6">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font> <b>by </b><i><a class="txt" href="filter_2.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a></i>;<br/><a NAME="E2:20_1"/>
<font color="Maroon" title="c5">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a'</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">b'</font>
 <b>by </b><i><a class="txt" href="filter_2.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:20_1"/>
( ( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) iff <font color="Maroon" title="c5">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="ref" href="filter_0.html#D1" title="FILTER_0:def.1">FILTER_0:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20"/>
<font color="Maroon" title="c3">x</font> is    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c2">L2</font>
 <b>by </b><i><a class="txt" href="filter_2.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="filter_0.html#D1" title="FILTER_0:def.1">FILTER_0:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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