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Proof step 76 from proof putarray-addarray-01 (previous step)

0 ≤ i2 ∧ 0 ≤ i, i→n(i2) + i→n(i) = n + i→n(i), 0 ≤ i2, 0 ≤ i2 + i, i2 < n→i(# vals), 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, 0 < n→i(# vals) + i, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ vals = [], vals[i→n(i2)] = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
0 < n→i(# vals) + i0, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i, 0 < i0, 0 ≤ i0 + i + n→i(# vals), 0 ≤ i0 + n→i(# vals), 0 ≤ i, i2 < n→i(# vals), 0 ≤ i2 + i, 0 ≤ i2 ⊦ vals[i→n(i2)] = (vals + mklist(initial_value(ty), i→n(i0)))[i→n(i2)], vals = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0])]]