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Proof step 9 from proof range (previous step)

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

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: range-last: ⊦ n ≠ 0 ∧ n < # zbrar → key-range(zbrar, n, n + 1, ri) = ri |> zbrar[n - 1].key;%range-inner: ⊦ n ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri) = (ri |> zbrar[n - 1].key) |≤ zbrar[n].key;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%succ-03: ⊦ m < n ∧ m + 1 ≠ n → m + 1 < n; (forward) from specification nat-basic