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Proof step 11 from proof ac-isarray (previous step)

sk .fs = mkfs(class, ty, fieldvar), ∀ r, i, class1, st. is_arrayref(r, i, addclass(class1, fis0, st)) ↔ is_arrayref(r, i, st) ⊦ is_arrayref(r, i, addclass(class1, (sk × val) ' + fis0, st)) ↔ is_arrayref(r, i, st), ¬ is_indexkey(sk) ∧ class ≠ class1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 8:
¬ is_indexkey((sk × val) .1), sk .fs = mkfs(class, ty, fieldvar), ∀ r, i, class1, st. is_arrayref(r, i, addclass(class1, fis0, st)) ↔ is_arrayref(r, i, st) ⊦ is_arrayref(r, i, addclass(class1, (sk × val) ' + fis0, st)) ↔ is_arrayref(r, i, st), ¬ is_indexkey(sk) ∧ class ≠ class1
Proof step 10:
is_indexkey((sk × val) .1), sk .fs = mkfs(class, ty, fieldvar), ∀ r, i, class1, st. is_arrayref(r, i, addclass(class1, fis0, st)) ↔ is_arrayref(r, i, st) ⊦ is_arrayref(r, i, addclass(class1, fis0, st)) ↔ is_arrayref(r, i, st), ¬ is_indexkey(sk) ∧ class ≠ class1

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0, sk × val, class1] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk × val, class1)]]