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Proof step 6 from proof add-at-gr (previous step)

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

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [st, ty, r, i, vals0] → [st, ty, r, i, vals .butlast]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n ≤ m ↔ n = 0], [CSIMPSEQ : n0 < n ⊦ m + ((* n)) ≤ m0 + ((* n0)) ↔ m + (n - n0) ≤ m0], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < 1 ↔ m = 0], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ vals ≠ [] → # vals .butlast = # vals - 1], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPFORWARD : ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j], [CSIMPFORWARD : ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ n→i(m) < n→i(n) ↔ m < n], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (st, ty, r, i, vals .butlast)]]