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Proof step 56 from proof putarray-addarray-01 (previous step)

i ≤ i1, n→i(# vals) + i ≤ i1, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, i1 < i + n→i(# vals) + i0, 0 ≤ i1, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ initial_value(ty) = (vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1) - i→n(i)]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
i→n(i1) = n + i→n(i) ∧ i→n(i) ≤ i→n(i1), i ≤ i1, n→i(# vals) + i ≤ i1, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, i1 < i + n→i(# vals) + i0, 0 ≤ i1, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ initial_value(ty) = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Rule argument

[speclemmaarg: n ≤ m ,n0 = m - n ↔ m = n0 + n ,[m, n, n0] → [i→n(i1), i→n(i), 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(i1), i→n(i), n)]]