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Proof step 5 from proof okarrays-all (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
sk0 .fs = mkfs(class0, ty0, fieldvar0), sk .fs = mkfs(class, ty, fieldvar), is_fskey(sk), is_arraytype(ty), okarray(st[r -- sk], ty .type, i, st), okarrays(r, fis0, st), sk0 × val0 ∈ fis0 ∨ sk0 = sk ∧ val0 = intval(i), ∀ 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) ⊦ is_integervalue(val0) ∧ ¬ is_indexkey(sk0) ∧ is_arraytype(ty0) ∧ okarray(st[r -- sk0], ty0 .type, val0 .intval, st)

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [sk0 .fs, class0, ty0, fieldvar0] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (sk0 .fs, class0, ty0, fieldvar0)]]