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Proof step 13 from proof okarrays-put (previous step)

sk0 .fs .type = mkarraytype(ty0), sk .fs = mkfs(class, ty, fieldvar), oktype(val, ty, st), goodfieldandtype(r0, sk, st), is_arraytype(sk0 .fs .type), ∀ sk, class, ty, fieldvar, val, st, r0, r. sk .fs = mkfs(class, ty, fieldvar) ∧ oktype(val, ty, st) ∧ goodfieldandtype(r0, sk, st) → sk = _type ∨ sk = _length ∨ (okarrays(r, fis0, st[r0 -- sk, val]) ↔ okarrays(r, fis0, st)) ∨ sk ∈ fis0 ⊦ sk = sk0, sk = _type, sk = _length, okarrays(r, fis0, st[r0 -- sk, val]) ∧ okarray(st[r -- sk0], ty0, i, st[r0 -- sk, val]) ∧ is_fskey(sk0) ↔ okarray(st[r -- sk0], ty0, i, st) ∧ okarrays(r, fis0, st) ∧ ¬ is_indexkey(sk0), sk ∈ fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
sk .fs = mkfs(class, ty, fieldvar), sk0 .fs .type = mkarraytype(ty0), goodfieldandtype(r0, sk, st), oktype(val, ty, st), ∀ sk, class, ty, fieldvar, val, st, r0, r. sk .fs = mkfs(class, ty, fieldvar) ∧ oktype(val, ty, st) ∧ goodfieldandtype(r0, sk, st) → sk = _type ∨ sk = _length ∨ (okarrays(r, fis0, st[r0 -- sk, val]) ↔ okarrays(r, fis0, st)) ∨ sk ∈ fis0 ⊦ okarrays(r, fis0, st[r0 -- sk, val]) ∧ okarray(st[r -- sk0], ty0, i, st[r0 -- sk, val]) ∧ is_fskey(sk0) ↔ okarray(st[r -- sk0], ty0, i, st) ∧ okarrays(r, fis0, st) ∧ ¬ is_indexkey(sk0), sk = _length, sk = _type, sk = sk0, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))])]]