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Proof step 45 from proof putarray-addarray-01 (previous step)

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])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
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])

Rule argument

[speclemmaarg: n ≤ m ,n0 = m - n ↔ m = n0 + n ,[m, n, n0] → [n, # vals, n0] ,T ,nat , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (n, # vals, n0)]]