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

okarrays(r, fis0, st), ∀ sk, val. sk × val ∈ fis0 → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st), ∀ sk0, val0. sk0 × val0 ∈ fis0 ∨ sk0 = sk ∧ val0 = val → is_integervalue(val0) ∧ ¬ is_indexkey(sk0) ∧ is_arraytype(sk0 .fs .type) ∧ okarray(st[r -- sk0], sk0 .fs .type .type, val0 .intval, st), sk .fs = mkfs(class, ty, fieldvar) ⊦ is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(ty) ∧ okarray(st[r -- sk], ty .type, val .intval, st) ∧ okarrays(r, fis0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
sk .fs = mkfs(class, ty, fieldvar), okarrays(r, fis0, st), ∀ sk, val. sk × val ∈ fis0 → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st), ∀ sk0, val0. sk0 × val0 ∈ fis0 ∨ sk0 = sk ∧ val0 = val → is_integervalue(val0) ∧ is_fskey(sk0) ∧ is_arraytype(sk0 .fs .type) ∧ okarray(st[r -- sk0], sk0 .fs .type .type, val0 .intval, st) ⊦ is_integervalue(val) ∧ ¬ is_indexkey(sk) ∧ is_arraytype(ty) ∧ okarray(st[r -- sk], ty .type, val .intval, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])]]