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<b>let </b><font color="Maroon">V</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/>







<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>,  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> =  <a href="lattice2.html#K2">FinJoin</a> <span class="p1">(<span class="default"><a href="heyting2.html#K6" target="_self">SUB</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">V</font>,<font color="Maroon">C</font>) <a href="funcop_1.html#K6">.:</a> <span class="p2">(<span class="default"><a href="heyting2.html#K4" target="_self">pseudo_compl</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="heyting2.html#K5" target="_self">StrongImpl</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> <a href="funcop_1.html#K7">[:]</a> <span class="p3">(<span class="default"><a href="heyting2.html#K7" target="_self">diff</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>,<font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E1:52"/>
( <font color="Maroon">u</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">u</font>,<font color="Maroon">v</font>) <a href="lattices.html#R3">[=</a> <font color="Maroon">v</font> &amp; ( for <font color="Olive">w</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>  st <font color="Maroon">u</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">w</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">v</font> holds <br/><font color="Olive">w</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">u</font>,<font color="Maroon">v</font>) ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:52"/>
<font color="Maroon">u</font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="lattice2.html#K2">FinJoin</a> <span class="p1">(<span class="default"><a href="heyting2.html#K6" target="_self">SUB</a> <font color="Maroon">u</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <span class="p2">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> <a href="funcop_1.html#K6">.:</a> <span class="p2">(<span class="default"><a href="heyting2.html#K4" target="_self">pseudo_compl</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="heyting2.html#K5" target="_self">StrongImpl</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> <a href="funcop_1.html#K7">[:]</a> <span class="p3">(<span class="default"><a href="heyting2.html#K7" target="_self">diff</a> <font color="Maroon">u</font></span>)</span>,<font color="Maroon">v</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>


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