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Proof step 59 from proof putarray-addarray-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
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) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i < i + j ↔ 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j = j + i])]]