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Proof step 42 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 '])) ↔ 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)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ okreftype(refval(r), mkarraytype(ty), addarray(r, ty, vals, st))
Proof step 7:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 8:
⊦ (addarray(r, ty, vals, st)[r -- _length]) = intval(n→i(# vals))
Proof step 9:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 41:
⊦ r = jvmref, 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 '])) ↔ is_arrayref(r, n→i(# vals), addarray(r, byte_type, vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < n→i(# vals) → is_bytevalue(vals[i→n(j)]))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]