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Proof step 19 from proof validref-ac (previous step)

sk .fs = mkfs(class0, ty0, fieldvar), ∀ str, r, ty, class, st. validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st) ⊦ validref(str, r, ty, addclass(class, (sk × val) ' + fis0, st)) ↔ validref(str, r, ty, st), ¬ is_indexkey(sk) ∧ class0 ≠ class

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 16:
¬ is_indexkey((sk × val) .1), sk .fs = mkfs(class0, ty0, fieldvar), ∀ str, r, ty, class, st. validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st) ⊦ validref(str, r, ty, addclass(class, (sk × val) ' + fis0, st)) ↔ validref(str, r, ty, st), ¬ is_indexkey(sk) ∧ class0 ≠ class
Proof step 18:
is_indexkey((sk × val) .1), sk .fs = mkfs(class0, ty0, fieldvar), ∀ str, r, ty, class, st. validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st) ⊦ validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st), ¬ is_indexkey(sk) ∧ class0 ≠ class

Rule argument

[speclemmaarg: , is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st) ,[st, fis, fv, class] → [st, fis0, sk × val, class] ,F ,addfuns , ,ac-no2 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk × val, class)]]