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Proof step 44 from proof okarray-init-04 (previous step)

⊦ okreftype(refval(r), mkarraytype(byte_type), addarray(r, byte_type, vals + byteval(by) ', st)) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i + 1) ∈ addarray(r, byte_type, vals + byteval(by) ', st) ∧ 0 ≤ i + 1 ∧ is_arrayref(refval(r) .refval, i + 1, addarray(r, byte_type, vals + byteval(by) ', st)) ∧ (∀ j. 0 ≤ j ∧ j < i + 1 → oktype (addarray(r, byte_type, vals + byteval(by) ', st)[refval(r) .refval -- j '], byte_type, addarray(r, byte_type, vals + byteval(by) ', st))) ↔ okarray(refval(r), byte_type, i, addarray(r, byte_type, vals, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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 43:
⊦ 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))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : i < 0 ⊦ ((* i)) ≤ n→i(n)], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]