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Proof step 56 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ i, i = n→i(n + i→n(j)), n < i→n(i1) + # bytes, n→i(# bytes) + j ≤ i, i < n→i(# bytes) + j + i1, i < n→i(# bytes) + i1 + j, 0 < n→i(# bytes) + i1 + j, 0 ≤ i, 0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1, 0 ≤ j + n→i(# bytes) + i1, i→n(i) < (i→n(i1) + # bytes) + i→n(j), 0 < i1, 0 < n→i(# bytes) + i1, j ≤ i ⊦ initial_value(byte_type) = (mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
0 < n→i(# bytes) + i1 + j, n→i(n) < n→i(# bytes) + i1, # bytes ≤ n, 0 < n→i(# bytes) + i1, 0 ≤ n→i(n) + j, n < i→n(i1) + # bytes, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 < i1 ⊦ initial_value(byte_type) = (mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[n], i1 = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i→n(i) = 0 ↔ i = 0], [CSIMPSEQ : ⊦ m < m + n ↔ n ≠ 0], [CSIMPFORWARD : ⊦ m ≤ n ∧ n < n0 → m < n0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + n→i(n)) = i→n(i) + n], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)])]]