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<b>let </b><font color="Maroon" title="c1">V</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">C</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>;<br/>







<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>,  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> =  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <span class="p1">(<span class="default"><a href="heyting2.html#K6" title="HEYTING2:func.6">SUB</a> $1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>) <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p2">(<span class="default"><a href="heyting2.html#K4" title="HEYTING2:func.4">pseudo_compl</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="heyting2.html#K5" title="HEYTING2:func.5">StrongImpl</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">[:]</a> <span class="p3">(<span class="default"><a href="heyting2.html#K7" title="HEYTING2:func.7">diff</a> $1</span>)</span>,$2</span>)</span></span>)</span>;<br/>
<a NAME="E1:51"/>
( <font color="Maroon" title="c3">u</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>) <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">v</font> &amp; ( for <font color="Olive" title="b1">w</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>  st <font color="Maroon" title="c3">u</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">w</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">v</font> holds <br/><font color="Olive" title="b1">w</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>) ) )
 
<b>by </b><i><a class="txt" href="heyting2.html#E50"><i><font color="Green" title="E41">Lm10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:51"/>
<font color="Maroon" title="c3">u</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <span class="p1">(<span class="default"><a href="heyting2.html#K6" title="HEYTING2:func.6">SUB</a> <font color="Maroon" title="c3">u</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p2">(<span class="default"><a href="heyting2.html#K4" title="HEYTING2:func.4">pseudo_compl</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="heyting2.html#K5" title="HEYTING2:func.5">StrongImpl</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">[:]</a> <span class="p3">(<span class="default"><a href="heyting2.html#K7" title="HEYTING2:func.7">diff</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a></i>;<br/>


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