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Proof step 1 from proof range-gt (conclusion)

⊦ n ≠ 0 ∧ n < nused ∧ key ≤ zbrar[n - 1].key ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri |> key) = key-range(zbrar, n, nused, ri)

System applied rule normalize

And obtained the following new goals

Proof step 2:
n < nused, key ≤ zbrar[n - 1].key, nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri |> key) = key-range(zbrar, n, nused, ri), n = 0

Rule argument

Additional information