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Proof step 16 from proof add-okarray (previous step)

⊦ r = val .refval, okreftype(val, mkarraytype(ty0), addarray(r, ty, vals, st)) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ addarray(r, ty, vals, st) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, addarray(r, ty, vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(addarray(r, ty, vals, st)[val .refval -- j '], ty0, addarray(r, ty, vals, st))) ↔ okarray(val, ty0, i, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ r ≠ r0 → ((r -- sk) × val ∈ addarray(r0, ty, vals, st) ↔ (r -- sk) × val ∈ st)
Proof step 3:
⊦ r ≠ r0 → (is_arrayref(r, i, addarray(r0, ty0, vals, st)) ↔ is_arrayref(r, i, st))
Proof step 4:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 15:
⊦ r = val .refval, okreftype(val, mkarraytype(ty0), addarray(r, ty, vals, st)) ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ 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 '], ty0, addarray(r, ty, vals, st))) ↔ okarray(val, ty0, i, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val])]]