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Proof step 9 from proof ac-okarrays (previous step)

sk .fs = mkfs(class0, mkarraytype(ty0), fieldvar), is_fskey(sk), is_integervalue(val), sk × val ∈ fis, okarray(st[r -- sk], ty0, val .intval, addclass(class, fis0, st)), ∀ sk, val. sk × val ∈ fis → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, addclass(class, fis0, st)) ⊦ r = jvmref, okarray(st[r -- sk], ty0, val .intval, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
sk = fs ', fs = mkfs(class0, mkarraytype(ty0), fieldvar), is_fskey(sk), is_integervalue(val), sk × val ∈ fis, okarray(st[r -- sk], ty0, val .intval, addclass(class, fis0, st)), ∀ sk, val. sk × val ∈ fis → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, addclass(class, fis0, st)) ⊦ r = jvmref, okarray(st[r -- sk], ty0, val .intval, st)

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]