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Proof step 20 from proof cut (previous step)

# ar = m + 1 ∧ # ar ≠ 0 ⊦ ar = [], # ar = m + 1 ∧ (n < # ar → ar[n] = copy(ar, 1, mkarray(m + 1), 1, m)[0, ar[0]][n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# ar = m + 1, n ≤ m ⊦ ar = [], ar[n] = copy(ar, 1, mkarray(m + 1), 1, m)[0, ar[0]][n]

Rule argument

Additional information

Used simplifier rules: le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1