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Step * 6 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 : free-dl-type(X)
7. b : free-dl-type(X)
8. 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)
BY
{ ((Subst' free-dl-join(a;free-dl-join(b;c)) ~ free-dl-join(free-dl-join(a;b);c) 0
    THENA (RepUR ``free-dl-join`` 0 THEN Auto)
    )
   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.  a  :  free-dl-type(X)
7.  b  :  free-dl-type(X)
8.  c  :  free-dl-type(X)
\mvdash{}  free-dl-join(a;free-dl-join(b;c))  =  free-dl-join(free-dl-join(a;b);c)


By

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Latex:
((Subst'  free-dl-join(a;free-dl-join(b;c))  \msim{}  free-dl-join(free-dl-join(a;b);c)  0
    THENA  (RepUR  ``free-dl-join``  0  THEN  Auto)
    )
  THEN  Auto
  )

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