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Proof step 58 from proof putByteArray-vals-addarray-01 (previous step)

i→n(i) = n + i→n(j) ∧ i→n(j) ≤ i→n(i), n→i(# bytes) + j ≤ i, 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 ⊦ 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 57:
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]

Rule argument

[emptyarg]

Additional information

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