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Proof step 2 from proof scan-entry-0 (previous step)

zbrar[n] = mkzentry(key, adr), n < len, sorted(zbrar, 0, nused), len ≤ nused, nused ≤ # zbrar ⊦ scan(key, zbrar, 0, len) = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
zbrar[n] = mkzentry(key, adr), n < nused, n < len, n < # zbrar, sorted(zbrar, 0, nused), len ≤ # zbrar, len ≤ nused, nused ≤ # zbrar ⊦ scan(key, zbrar, 0, len) = n

Rule argument

Additional information

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