lean2/tests/lean/run/vec_inv2.lean

30 lines
751 B
Text
Raw Normal View History

import data.nat.basic data.empty data.prod
open nat eq.ops prod
inductive vector (T : Type) : → 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 :=
begin
cases v,
apply Hnil
end
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 :=
begin
cases v with (h', n', t'),
apply (H h' t')
end
end vector