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Proof step 141 from proof putarray-addarray-override (previous step)

n→i(n) + i < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], vals0[i→n(i) + n] = (restn(i→n(i) + # vals, vals0)[n - # vals])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 140:
n = n0 + # vals, n→i(n) + i < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], vals0[i→n(i) + n] = (restn(i→n(i) + # vals, vals0)[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)]]