Fixpoint nth_error_opt {A : Type} {m : nat} (v : Vector.t A m) (n : nat) : option A :=
  match n with
  | O =>
    match v with
    | Vector.nil _ => None
    | Vector.cons _ h _ _ => Some h
    end
  | S p =>
    match v with
    | Vector.nil _ => None
    | Vector.cons _ _ n1 t0 => nth_error_opt t0 p
    end
  end.

Lemma nth_error_opt_some: forall {A : Type} {m : nat} (v : Vector.t A m) (n : nat) (a : A), nth_error_opt v n = Some a -> Nat.lt n m.