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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    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:72"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>3</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D12">LATTICES:def 12</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <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 <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D12">LATTICES:def 12</a><br/>

<b>assume </b><a NAME="E2:72"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="filter_0.html#T63" target="_self">Th63</a></i>;<br/>
<a NAME="E4:72"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T64" target="_self">Th64</a></i>;<br/>
<a NAME="E5:72"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="filter_0.html#E2:72"><i><font color="Green">E51</font></i></a>, <a class="ref" href="filter_0.html#T64" target="_self">Th64</a>, <a class="ref" href="filter_0.html#T65" target="_self">Th65</a></i>;<br/>
<b>hence </b><a NAME="E6:72"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="filter_0.html#E1:72"><i><font color="Green">E50</font></i></a></i>;<br/>


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