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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">F</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:85"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon" title="c1">L</font> is   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D1" title="RELAT_2:def.1">RELAT_2:def 1</a><br/>

<b>assume </b><a NAME="E2:85"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E4:85"/>
<font color="Maroon" title="c4">p</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="filter_0.html#E1:85"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="filter_0.html#T38" target="_self" title="FILTER_0:th.38">Th38</a></i>;<br/>
<a NAME="E5:85"/><b>then </b><i><font color="Green" title="E62">A2</font></i>: 
<font color="Maroon" title="c4">p</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T18" title="LATTICES:th.18">LATTICES:18</a></i>;<br/>
<a NAME="E6:85"/>
<font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a>
 
<b>by </b><i><a class="txt" href="filter_0.html#E1:85"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="filter_0.html#T37" target="_self" title="FILTER_0:th.37">Th37</a></i>;<br/>
<a NAME="E7:85"/><b>then </b>
<font color="Maroon" title="c4">p</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="txt" href="filter_0.html#E5:85"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="filter_0.html#T12" target="_self" title="FILTER_0:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E8:85"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="ref" href="filter_0.html#D12" target="_self" title="FILTER_0:def.12">Def12</a></i>;<br/>


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