import data.nat.basic data.empty data.prod open nat eq.ops prod inductive vector (T : Type) : ℕ → Type := | nil {} : vector T 0 | cons : T → ∀{n}, vector T n → vector T (succ n) set_option pp.metavar_args true set_option pp.implicit true set_option pp.notation false namespace vector variables {A B C : Type} variables {n m : nat} theorem z_cases_on {C : vector A 0 → Type} (v : vector A 0) (Hnil : C nil) : C v := by cases v; apply Hnil protected definition destruct (v : vector A (succ n)) {P : Π {n : nat}, vector A (succ n) → Type} (H : Π {n : nat} (h : A) (t : vector A n), P (cons h t)) : P v := by cases v with [h', n', t']; apply (H h' t') end vector