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Step * 9 2 1 of Lemma free-dl_wf

.....assertion..... 
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. X List List ∈ Type
10. ∀as,bs:X List List.  (dlattice-eq(X;as;bs) ∈ Type)
11. ∀as:X List List. dlattice-eq(X;as;as)
12. as : X List List
13. bs : X List List
14. dlattice-eq(X;as;bs)
15. free-dl-type(X) = free-dl-type(X) ∈ Type
⊢ free-dl-meet([[]];as) = as ∈ (X List List)
BY
{ (RepUR ``free-dl-meet`` 0 THEN All Thin) }

1
1. X : Type
2. as : X List List
⊢ map(λb.b;as) = as ∈ (X List List)

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Latex:

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Latex:
.....assertion..... 
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.  X  List  List  \mmember{}  Type
10.  \mforall{}as,bs:X  List  List.    (dlattice-eq(X;as;bs)  \mmember{}  Type)
11.  \mforall{}as:X  List  List.  dlattice-eq(X;as;as)
12.  as  :  X  List  List
13.  bs  :  X  List  List
14.  dlattice-eq(X;as;bs)
15.  free-dl-type(X)  =  free-dl-type(X)
\mvdash{}  free-dl-meet([[]];as)  =  as


By

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Latex:
(RepUR  ``free-dl-meet``  0  THEN  All  Thin)

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