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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>, <font color="Maroon">c<sub>4</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:59"/>
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span>
 
<b>by </b><i><a class="ref" href="filter_2.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E2:59"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E3:59"/>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> implies <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> ) &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><span class="p2"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> )
 <b>by </b><i><a class="ref" href="filter_2.html#D11" target="_self">Def11</a></i>;<br/>


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