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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">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:76"/>
 <a href="filter_0.html#K8" target="_self">latt</a> <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span> is   <a href="lattices.html#NM4">0_Lattice</a>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">q'</font> being   <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> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span><b> such that </b><br/><a NAME="E3:76"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">r'</font> being  <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> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> holds <br/> ( <font color="Maroon">q'</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">r'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font> &amp; <font color="Olive">r'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font> )
 <b>by </b><i><a class="ref" href="lattices.html#D13">LATTICES:def 13</a></i>;<br/>
<a NAME="E4:76"/><i><font color="Green">E42</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span>
 
<b>by </b><i><a class="ref" href="filter_0.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E5:76"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">q'</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="filter_0.html#T19" target="_self">Th19</a>, <a class="ref" href="rlsub_2.html#T84">RLSUB_2:84</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font> as   <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> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> <b>by </b><i><a class="ref" href="filter_0.html#T20" target="_self">Th20</a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q'</font> as    <a href="subset_1.html#M2">Element</a> of <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span> <b>by </b><i><a class="ref" href="filter_0.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E8:76"/>
<font color="Maroon">q'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E9:76"/><b>then </b>
<font color="Maroon">q'</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">p'</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T21">LATTICES:21</a></i>;<br/>
<a NAME="E10:76"/><b>then </b>
( <font color="Maroon">q</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font> )
 
<b>by </b><i>, <a class="ref" href="filter_0.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E11:76"/>
 <a href="lattices.html#K5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>


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