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Proof step 44 from proof putarray-addarray-01 (previous step)

n = n0 + # vals, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, n→i(n) < n→i(# vals) + i0, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0, # vals ≤ n, 0 ≤ n→i(n) + i ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i0))[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, n→i(n0) < i0, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0, 0 ≤ (n→i(n0) + n→i(# vals)) + i ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i0))[n0])

Rule argument

[emptyarg]

Additional information

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