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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> 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/>



<b>assume </b><a NAME="E1:31"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM4">0_Lattice</a> &amp;  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:31"/><b>then </b><i><font color="Green">E24</font></i>: 
( <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="filter_0.html#K2" target="_self">.)</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_0.html#K1" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_0.html#K1" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="filter_0.html#K2" target="_self">.)</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K3" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_0.html#K1" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_0.html#K1" target="_self">.)</a></span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T20" target="_self">Th20</a>, <a class="ref" href="filter_0.html#T29" target="_self">Th29</a></i>;<br/>
<b>hence </b><a NAME="E3:31"/>
( <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K3" target="_self">.)</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K1" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_0.html#K1" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_0.html#K1" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_0.html#K1" target="_self">.)</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K3" target="_self">.)</a></span> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E4:31"/>
( <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K3" target="_self">.)</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K3" target="_self">.)</a></span> )
 <b>by </b><i><a class="txt" href="filter_0.html#E2:31"><i><font color="Green">E24</font></i></a></i>; <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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