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Proof step 7 from proof okarrays-all (previous step)

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), sk0 × val0 ∈ fis0 ∨ sk0 = sk ∧ val0 = val, ∀ 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 6:
val = intval(i), sk .fs = mkfs(class, ty, fieldvar), is_integervalue(val), is_fskey(sk), is_arraytype(ty), okarray(st[r -- sk], ty .type, i, st), okarrays(r, fis0, st), sk0 × val0 ∈ fis0 ∨ sk0 = sk ∧ val0 = val, ∀ 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)

Rule argument

[speclemmaarg: ,is_integervalue(val) → (i = val .intval ↔ val = intval(i)) ,[val, i] → [val, i] ,T ,javavalue , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (val, i)]]