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Proof step 4 from proof scan-strong (previous step)

scan(key, zbrar, 0, nused) < n0, n0 < nused, sorted(zbrar, 0, nused), scan(key, zbrar, 0, nused) ≤ # zbrar, scan(key, zbrar, 0, nused) ≤ nused, nused ≤ # zbrar ⊦ key < zbrar[n0].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
scan(key, zbrar, 0, nused) < # zbrar, scan(key, zbrar, 0, nused) + 1 < nused, n0 < nused, scan(key, zbrar, 0, nused) < n0, n0 < # zbrar, scan(key, zbrar, 0, nused) < nused, scan(key, zbrar, 0, nused) + 1 < # zbrar, sorted(zbrar, 0, nused), nused ≤ # zbrar ⊦ key < zbrar[n0].key

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic