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Proof step 9 from proof okarray-1dim-02 (previous step)

⊦ r = r0, okreftype(refval(r), mkarraytype(int_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(r, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_integervalue(st[r -- j '])) ↔ okarray(refval(r), int_type, i, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 8:
⊦ r = r0, okreftype(refval(r), mkarraytype(int_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(r, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_integervalue(st[r -- j '])) ↔ okreftype(refval(r), mkarraytype(int_type), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[refval(r) .refval -- j '], int_type, 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, int_type, refval(r)] ,F ,okfuns , ,okarrayOfLength ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i, int_type, refval(r))]]