Section vec_nat_induction.
(* Specialized induction on vec nat n, with constant n *)
Variable (n : nat) (P : vec nat n -> Type).
Hypothesis HP0 : P vec_zero.
Hypothesis HP1 : forall p, P (vec_one p).
Hypothesis HP2 : forall v w, P v -> P w -> P (vec_plus v w).

Theorem vec_nat_induction v : P v.