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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  non <a href="xboole_0.html#V1">empty</a>  <a href="lattice4.html#M2">ClosedSubset</a> of <font color="Maroon">L</font>;<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/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<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_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</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_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:104"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font> )
 ;<br/>

<b>consider </b><font color="Maroon">o1</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font>, <font color="Maroon">o2</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font><b> such that </b><br/><a NAME="E3:104"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">P</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">L</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">P</font> &amp;  <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">o1</font>,<font color="Maroon">o2</font> #) )
 <b>by </b><i><a class="ref" href="filter_2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E4:104"/><i><font color="Green">E16</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">P</font>,<font color="Maroon">P</font></span><a href="mcart_1.html#K12">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">P</font>,<font color="Maroon">P</font></span><a href="mcart_1.html#K12">:]</a></span> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">p'</font>,<font color="Maroon">q'</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">P</font>,<font color="Maroon">P</font></span><a href="mcart_1.html#K12">:]</a></span> )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><a NAME="E5:104"/>
<font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q'</font>
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/>

<b>thus </b><a NAME="E6:104"/>
<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>
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/>


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