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Proof step 73 from proof putarray-addarray-01 (previous step)

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 = [], vals[i→n(i2)] = (mklist(initial_value(ty), i→n(i0))[i→n(i2) - # vals])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 72:
i→n(i2) = n + # vals, 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 = [], vals[i→n(i2)] = (mklist(initial_value(ty), i→n(i0))[n])

Rule argument

[speclemmaarg: n ≤ m ,n0 = m - n ↔ m = n0 + n ,[m, n, n0] → [i→n(i2), # vals, n] ,T ,nat , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (i→n(i2), # vals, n)]]