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

<b>assume </b><a NAME="E1:20"/><i><font color="Green">E14</font></i>: 
 <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L1</font> #) <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L2</font> #)
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E2:20"/>
<font color="Maroon">x</font> is    <a href="filter_2.html#M1" target="_self">Filter</a> of <font color="Maroon">L1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">F</font> = <font color="Maroon">x</font> as    <a href="filter_2.html#M1" target="_self">Filter</a> of <font color="Maroon">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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/><b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/><a NAME="E2:20_1"/>
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b'</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:20_1"/>
( ( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> ) iff <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 <b>by </b><i><a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20"/>
<font color="Maroon">x</font> is    <a href="filter_2.html#M1" target="_self">Filter</a> of <font color="Maroon">L2</font>
 <b>by </b><i>, <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>


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