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Proof step 3 from proof range-last-2 (previous step)

n + 1 < # zbrar ⊦ key-range(zbrar, n + 1, n + 2, ri) = ri |> zbrar[n].key

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: range-last seq: ⊦ n ≠ 0 ∧ n < # zbrar → key-range(zbrar, n, n + 1, ri) = ri |> zbrar[n - 1].key subst: [n, zbrar, ri] → [n + 1, zbrar, ri]

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s) Used terms: n + 1, zbrar, ri