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Proof step 1 from proof range (conclusion)

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

System applied rule normalize

And obtained the following new goals

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

Proof step 1 from proof range (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information