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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">D</font> be  <a href="lattice3.html#V4" target="_self">complete</a> <a href="lattice3.html#V5" target="_self">\/-distributive</a> <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font>;<br/>





<a NAME="E1:90"/><i><font color="Green">E18</font></i>: 
(  <a href="lattice3.html#K15" target="_self">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> ,<font color="Maroon">D</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" target="_self">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">D</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" target="_self">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">D</font></span>)</span> <a href="lattices.html#R3">[=</a>  <a href="lattice3.html#K15" target="_self">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> ,<font color="Maroon">D</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#T2" target="_self">Th2</a>, <a class="ref" href="lattice3.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E2:90"/>
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" target="_self">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K15" target="_self">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> ,<font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>

<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">D</font> = <font color="Maroon">a<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">D</font> = <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>;<br/>
<a NAME="E3:90"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> holds  <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b</font>)
 
;<br/>
<a NAME="E4:90"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b</font>) where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">c</font>) where <font color="Olive">c</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">c</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S5">FRAENKEL:sch 5</a>(<a class="ref" href="lattice3.html#T7" target="_self">Th7</a>);<br/></i>
<b>hence </b><a NAME="E5:90"/>
<span class="p1">(<span class="default"><a href="lattice3.html#K15" target="_self">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">D</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K15" target="_self">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font></span>)</span> where <font color="Olive">b2</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">b2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> ,<font color="Maroon">D</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>


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