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Proof step 27 from proof move-initvals (previous step)

0 ≤ i, i→n(i) < # vals, ∀ val, st, ty, r, i, vals0. # vals0 < # vals → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ vals = [], (addarray(r, ty, vals .butlast, st)[r -- n→i(# vals - 1) ', vals .last][r -- _length, intval(n→i(# vals))][r -- i ', val]) = addarray(r, ty, vals[i→n(i), val], st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
# vals = m + 1 ∧ # vals ≠ 0, 0 ≤ i, i→n(i) < # vals, ∀ val, st, ty, r, i, vals0. # vals0 < # vals → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ vals = [], (addarray(r, ty, vals .butlast, st)[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(# vals))][r -- i ', val]) = addarray(r, ty, vals[i→n(i), val], st)

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)]]