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Proof step 16 from proof okarray-init-basic-01 (previous step)

⊦ r = r0, okarray(refval(r), ty, i, addarray(r0, vals, j, st)) ↔ okarray(refval(r), ty, i, st), is_classtype(ty), is_arraytype(ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 15:
⊦ r = r0, okreftype(refval(r), mkarraytype(ty), addarray(r0, vals, j, st)) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ addarray(r0, vals, j, st) ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, addarray(r0, vals, j, st)) ∧ (∀ j0. 0 ≤ j0 ∧ j0 < i → oktype(addarray(r0, vals, j, st)[refval(r) .refval -- j0 '], ty, addarray(r0, vals, j, st))) ↔ okarray(refval(r), ty, i, st), is_classtype(ty), is_arraytype(ty)

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(r0, vals, j, st), i, ty, refval(r)] ,F ,okfuns , ,okarrayOfLength ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r0, vals, j, st), i, ty, refval(r))]]