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Proof step 43 from proof okarray-init-04 (previous step)

⊦ r ≠ jvmref ∧ n→i(# vals) = i ∧ is_arrayref(r, n→i(# vals) + 1, addarray(r, byte_type, vals + byteval(by) ', st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ n→i(# vals) < j → is_bytevalue(addarray(r, byte_type, vals + byteval(by) ', st)[r -- j '])) ↔ okarray(refval(r), byte_type, i, addarray(r, byte_type, vals, 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 42:
⊦ r ≠ jvmref ∧ n→i(# vals) = i ∧ is_arrayref(r, n→i(# vals) + 1, addarray(r, byte_type, vals + byteval(by) ', st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ n→i(# vals) < j → is_bytevalue(addarray(r, byte_type, vals + byteval(by) ', st)[r -- j '])) ↔ okreftype(refval(r), mkarraytype(byte_type), addarray(r, byte_type, vals, st)) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ addarray(r, byte_type, vals, st) ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, addarray(r, byte_type, vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(addarray(r, byte_type, vals, st)[refval(r) .refval -- j '], byte_type, addarray(r, byte_type, vals, 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] → [addarray(r, byte_type, vals, st), i, byte_type, refval(r)] ,F ,okfuns , ,okarrayOfLength ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, byte_type, vals, st), i, byte_type, refval(r))]]