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Proof step 11 from proof ac-okarray-01 (previous step)

⊦ val = refval(jvmref), okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ addclass(class, fis, st) ∧ st[val .refval -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[val .refval -- j '], ty, st)) ↔ okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[val .refval -- j '], ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ rk ∈ st → rk ∈ addclass(class, fis, st)
Proof step 10:
st[val .refval -- _length] = intval(i), okreftype(val, mkarraytype(ty), st), is_arrayref(val .refval, i, st), j < i, val .refval -- _length ∈ st, 0 ≤ i, 0 ≤ j, 0 < i, val .refval ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[val .refval -- j '], ty, st) ⊦ val = refval(jvmref), val .refval = jvmref, oktype(st[val .refval -- j '], ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ intval(i) ≠ noval], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val])]]