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Proof step 10 from proof scan-strong (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
scan(key, zbrar, 0, nused) < nused, zbrar[scan(key, zbrar, 0, nused)].key < key, scan(key, zbrar, 0, nused) < # zbrar, sorted(zbrar, 0, nused), nused ≤ # zbrar ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ 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% ⊦ m < n → m ≤ n; (s)