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Proof step 59 from proof putByteArray-vals-addarray-01 (previous step)

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)))[i→n(i) - i→n(j)]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
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]

Rule argument

[speclemmaarg: n ≤ m ,n0 = m - n ↔ m = n0 + n ,[m, n, n0] → [i→n(i), i→n(j), n] ,T ,nat , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (i→n(i), i→n(j), n)]]