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Proof step 7 from proof okarray-init-05 (conclusion)

⊦ r ≠ jvmref → okarray(refval(r), byte_type, 1, addarray(r, byte_type, byteval(by) ', st))

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 2:
⊦ okreftype(refval(r), mkarraytype(ty), addarray(r, ty, vals, st))
Proof step 3:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 4:
⊦ (addarray(r, ty, vals, st)[r -- _length]) = intval(n→i(# vals))
Proof step 5:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)
Proof step 6:
⊦ (addarray(r, ty, val ', st)[r -- 0 ']) = val

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, byteval(by) ', st), 1, byte_type, refval(r)] ,F ,okfuns , ,okarrayOfLength ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0], [CSIMPSEQ : ⊦ is_arrayref(r, 1, st) ↔ r -- 0 ' ∈ st], [CSIMPSEQ : ⊦ 0 ≤ i → (i < 1 ↔ i = 0)], [CSIMPSEQ : ⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)], [CSIMPSEQ : ⊦ is_bytevalue(byteval(by))])], [EXTRATERMS : (addarray(r, byte_type, byteval(by) ', st), 1, byte_type, refval(r))]]