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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM4">0_Lattice</a>;<br/>

<a NAME="E1:86"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="lattice2.html#NM2">H_Lattice</a> iff <font color="Maroon">c<sub>1</sub></font> is   <a href="filter_0.html#NM2">I_Lattice</a> )
 
<b>by </b><i><a class="ref" href="lattice2.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E2:86"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="lattice2.html#NM2">H_Lattice</a> iff for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>3</sub></font> ) ) )
 <b>by </b><i><a class="ref" href="filter_0.html#D7">FILTER_0:def 7</a></i>;<br/>


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