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Theorem scan-strong

nused ≤ # zbrar, sorted(zbrar, 0, nused), n = scan(key, zbrar, 0, nused) ⊦ n ≤ nused ∧ (n < nused → key ≤ zbrar[n].key) ∧ (∀ n0. n0 < n → zbrar[n0].key < key) ∧ (∀ n1. n < n1 ∧ n1 < nused → key < zbrar[n1].key)

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