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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">D1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">D2</font> be  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="48_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">D1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">D2</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>thus </b><a NAME="E1:48_1"/>
<font color="Maroon">D1</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:48_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D2</font>
 ;<br/>

<a NAME="E2:48_1_1"/><b>then </b>
 ex <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">q</font> &amp; <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> &amp; <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> )
 
;<br/>
<b>hence </b><a NAME="E3:48_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D1</font>
 ;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:48"/>
( <font color="Maroon">D1</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D1</font> &amp; <font color="Maroon">D2</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D1</font> <a href="filter_0.html#K5" target="_self">"/\"</a> <font color="Maroon">D2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>


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