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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>assume </b><a NAME="E1:20"/>
<font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM4">0_Lattice</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="lattices.html#NM4">0_Lattice</a> ;<br/>
<b>thus </b><a NAME="E3:20"/>
<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#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>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></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="E1:20_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</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>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E3:20_1"/>
(  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <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> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T40">LATTICES:40</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <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>
 <b>by </b><i><a class="ref" href="filter_0.html#D1" target="_self">Def1</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:20"/>
<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#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>
 ;<br/>


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