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Step * 10 of Lemma free-dl_wf


1. X : Type
2. EquivRel(X List List;as,bs.dlattice-eq(X;as;bs))
3. ∀[a,b:free-dl-type(X)].  (free-dl-meet(a;b) = free-dl-meet(b;a) ∈ free-dl-type(X))
4. ∀[a,b:free-dl-type(X)].  (free-dl-join(a;b) = free-dl-join(b;a) ∈ free-dl-type(X))
5. ∀[a,b,c:free-dl-type(X)].  (free-dl-meet(a;free-dl-meet(b;c)) = free-dl-meet(free-dl-meet(a;b);c) ∈ free-dl-type(X))
6. ∀[a,b,c:free-dl-type(X)].  (free-dl-join(a;free-dl-join(b;c)) = free-dl-join(free-dl-join(a;b);c) ∈ free-dl-type(X))
7. ∀[a,b:free-dl-type(X)].  (free-dl-join(a;free-dl-meet(a;b)) = a ∈ free-dl-type(X))
8. ∀[a,b:free-dl-type(X)].  (free-dl-meet(a;free-dl-join(a;b)) = a ∈ free-dl-type(X))
9. ∀[a:free-dl-type(X)]. (free-dl-meet(a;[[]]) = a ∈ free-dl-type(X))
10. a : free-dl-type(X)
⊢ free-dl-join(a;[]) = a ∈ free-dl-type(X)
BY
{ ((newQuotientElim (-1) THENA Auto) THEN RepUR ``free-dl-join`` 0 THEN RWO "append-nil" 0 THEN Auto) }

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Latex:

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Latex:

1.  X  :  Type
2.  EquivRel(X  List  List;as,bs.dlattice-eq(X;as;bs))
3.  \mforall{}[a,b:free-dl-type(X)].    (free-dl-meet(a;b)  =  free-dl-meet(b;a))
4.  \mforall{}[a,b:free-dl-type(X)].    (free-dl-join(a;b)  =  free-dl-join(b;a))
5.  \mforall{}[a,b,c:free-dl-type(X)].
          (free-dl-meet(a;free-dl-meet(b;c))  =  free-dl-meet(free-dl-meet(a;b);c))
6.  \mforall{}[a,b,c:free-dl-type(X)].
          (free-dl-join(a;free-dl-join(b;c))  =  free-dl-join(free-dl-join(a;b);c))
7.  \mforall{}[a,b:free-dl-type(X)].    (free-dl-join(a;free-dl-meet(a;b))  =  a)
8.  \mforall{}[a,b:free-dl-type(X)].    (free-dl-meet(a;free-dl-join(a;b))  =  a)
9.  \mforall{}[a:free-dl-type(X)].  (free-dl-meet(a;[[]])  =  a)
10.  a  :  free-dl-type(X)
\mvdash{}  free-dl-join(a;[])  =  a


By

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Latex:
((newQuotientElim  (-1)  THENA  Auto)  THEN  RepUR  ``free-dl-join``  0  THEN  RWO  "append-nil"  0  THEN  Auto)

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