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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM8">B_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="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:59"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font> ) )
 
<b>by </b><i><a class="ref" href="filter_0.html#T34" target="_self">Th34</a></i>;<br/>
<a NAME="E2:59"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="filter_0.html#V3" target="_self">implicative</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D7" target="_self">FILTER_0:def 7</a><br/>

<b>take </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>thus </b><a NAME="E1:59_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="ref" href="filter_0.html#T34" target="_self">Th34</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:59"/>
<font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#K4" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="filter_0.html#E1:59"><i><font color="Green">E42</font></i></a>, <a class="ref" href="filter_0.html#D8" target="_self">Def8</a></i>;<br/>


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