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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>





<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></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="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> =  <a href="lattice2.html#K2">FinJoin</a> <span class="p1">(<span class="default"><a href="heyting1.html#K10" 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>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funcop_1.html#K6">.:</a> <span class="p2">(<span class="default"><a href="heyting1.html#K8" target="_self">pseudo_compl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="heyting1.html#K9" target="_self">StrongImpl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funcop_1.html#K7">[:]</a> <span class="p3">(<span class="default"><a href="heyting1.html#K11" 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="E1:47"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>) <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>) ) )
 
<b>by </b><i><a class="txt" href="heyting1.html#E53"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:47"/>
<font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattice2.html#K2">FinJoin</a> <span class="p1">(<span class="default"><a href="heyting1.html#K10" target="_self">SUB</a> <font color="Maroon">c<sub>2</sub></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="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funcop_1.html#K6">.:</a> <span class="p2">(<span class="default"><a href="heyting1.html#K8" target="_self">pseudo_compl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="heyting1.html#K9" target="_self">StrongImpl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funcop_1.html#K7">[:]</a> <span class="p3">(<span class="default"><a href="heyting1.html#K11" target="_self">diff</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></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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