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Proof step 15 from proof add-okarray (previous step)

⊦ 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ okarray(val, ty, i, 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))
Proof step 14:
⊦ 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))) ↔ okreftype(val, mkarraytype(ty0), 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 '], ty0, st))

Rule argument

[speclemmaarg: , okarray(val, ty, i, 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)) ,[st, i, ty, val] → [st, i, ty0, val] ,F ,okfuns , ,okarrayOfLength ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i, ty0, val)]]