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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> be    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="filter_0.html#NM2">I_Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



















<b>thus </b><a NAME="E1:96"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#R1" target="_self">are_equivalence_wrt</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#R1" target="_self">are_equivalence_wrt</a> <font color="Maroon">c<sub>7</sub></font> implies <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#R1" target="_self">are_equivalence_wrt</a> <font color="Maroon">c<sub>7</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:96_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D13" target="_self">FILTER_0:def 13</a><br/>

<b>hence </b><a NAME="E2:96_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="filter_0.html#T78" target="_self">Th78</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D13" target="_self">FILTER_0:def 13</a><br/>


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

<a NAME="E2:96"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is   <a href="filter_0.html#NM2">I_Lattice</a>
 
<b>by </b><i><a class="ref" href="filter_0.html#T40" target="_self">Th40</a></i>;<br/>
<b>assume </b><a NAME="E3:96"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D13" target="_self">FILTER_0:def 13</a><br/>

<b>hence </b><a NAME="E4:96"/>
<font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="filter_0.html#E2:96"><i><font color="Green">E64</font></i></a>, <a class="ref" href="filter_0.html#T78" target="_self">Th78</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D13" target="_self">FILTER_0:def 13</a><br/>


</div>
