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<b>reconsider </b><font color="Maroon">D</font> =  <a href="filter_2.html#K12" target="_self">.:</a> <font color="Maroon">F</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><a NAME="E1:34_1_1_1"/>
(  <a href="filter_2.html#K12" target="_self">.:</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> ) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) &amp; <font color="Maroon">p</font> <a href="filter_2.html#K5" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">q</font> <a href="filter_2.html#K5" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp; <font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font> &amp; ( for <font color="Olive">p'</font>, <font color="Olive">q'</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span> holds <br/> ( ( <font color="Olive">p'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Olive">q'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> ) iff <font color="Olive">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">q'</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/><b>hence </b><a NAME="E2:34_1_1_1"/>
( ( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> ) iff <font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:34_1_1"/>
 <a href="filter_2.html#K8" target="_self">.:</a> <font color="Maroon">F</font> is    <a href="filter_2.html#M2" target="_self">Ideal</a> of <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="filter_2.html#T1" target="_self">Th1</a></i>;<br/>


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