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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:3"/><i><font color="Green">E1</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="filter_0.html#K3">.)</a></span>
 
<b>by </b><i><a class="ref" href="filter_0.html#D5">FILTER_0:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:3"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> )
 <b>by </b><i><a class="txt" href="lattice4.html#E1:3"><i><font color="Green">E1</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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