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Proof step 2 from proof sorted-2 (previous step)

m - n = 2, ar[n] ≤ ar[n + 1], m ≤ # ar ⊦ sorted(ar, n, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m - n = 2, ar[n0 + 1] < ar[n0], n0 + 1 < m, n0 + 1 < # ar, m ≤ # ar, n ≤ n0 ⊦ ar[n + 1] < ar[n]

Rule argument

Additional information

Used simplifier rules: less-eq-elem: ⊦ x ≤ y ↔ ¬ y < x;%sorted: ⊦ sorted(ar, n, m) ↔ m ≤ # ar ∧ (∀ n0. n ≤ n0 ∧ n0 + 1 < m → ar[n0] ≤ ar[n0 + 1]);% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic