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Proof step 10 from proof add-at-neg (previous step)

i < 0, ∀ st, ty, r, i, vals0. # vals0 < # vals → (i < 0 → (addarray(r, ty, vals0, st)[r -- i ']) = st[r -- i ']) ⊦ vals = [], ((i = n→i(# vals - 1) ⊃ vals .last; addarray(r, ty, vals .butlast, st)[r -- i '])) = st[r -- i ']

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
# vals = m + 1 ∧ # vals ≠ 0, i < 0, ∀ st, ty, r, i, vals0. # vals0 < # vals → (i < 0 → (addarray(r, ty, vals0, st)[r -- i ']) = st[r -- i ']) ⊦ vals = [], ((i = n→i(m) ⊃ vals .last; addarray(r, ty, vals .butlast, st)[r -- i '])) = st[r -- i ']

Rule argument

[speclemmaarg: n ≠ 0 ,m = n - 1 ↔ n = m + 1 ,[n, m] → [# vals, m] ,T ,nat , ,elim-pred-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPELIM : n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1])], [EXTRATERMS : (# vals, m)]]