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Proof step 55 from proof putarray-addarray-01 (previous step)

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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
i→n(i1) = n + i→n(i), 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, i ≤ i1 ⊦ initial_value(ty) = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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)])]]