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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:73"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font>, <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">p</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">q</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">r</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">q</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">r</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a><br/>

<b>let </b><font color="Maroon">p'</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">F</font></span>)</span>, <font color="Maroon">q'</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">F</font></span>)</span>, <font color="Maroon">r'</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">F</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a><br/>

<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">p'</font>, <font color="Maroon">q</font> = <font color="Maroon">q'</font>, <font color="Maroon">r</font> = <font color="Maroon">r'</font>, <font color="Maroon">qr</font> = <font color="Maroon">q'</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r'</font> as    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">F</font> <b>by </b><i><a class="ref" href="filter_0.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E3:73"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font> &amp; <font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T11" target="_self">Th11</a></i>;<br/>
<b>thus </b><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">q'</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r'</font></span>)</span> = 
<font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">qr</font>
<b>by </b><i><a class="ref" href="filter_0.html#T11" target="_self">Th11</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r</font></span>)</span>
<b>by </b><i><a class="ref" href="filter_0.html#T11" target="_self">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q'</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">r'</font></span>)</span>
<b>by </b><i><a class="ref" href="filter_0.html#T18" target="_self">Th18</a>, <a class="ref" href="filter_0.html#T11" target="_self">Th11</a></i>
;<br/>


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