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Proof step 46 from proof putarray-addarray-01 (previous step)

¬ n < # 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) = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
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))[n - # vals])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ ¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals]])]]