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Step * 9 1 of Lemma free-dl_wf

.....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-type(X)
BY
{ (SubsumeC ⌜X List List⌝⋅ THEN Auto) }

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Latex:

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Latex:
.....wf..... 
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.  a  :  free-dl-type(X)
\mvdash{}  [[]]  \mmember{}  free-dl-type(X)


By

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Latex:
(SubsumeC  \mkleeneopen{}X  List  List\mkleeneclose{}\mcdot{}  THEN  Auto)

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