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Proof step 26 from proof move-initvals (previous step)

# 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# vals = m + 1, i→n(i) ≤ m, 0 ≤ i, ∀ val, st, ty, r, i, vals0. # vals0 < m + 1 → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ (addarray(r, ty, vals .butlast, st)[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)][r -- i ', val]) = addarray(r, ty, vals[i→n(i), val], st), vals = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n = n0 → m < n0], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []])]]