Section In_Dec.
Variable X : Type.
Hypothesis X_dec : eq_dec X.
Fixpoint in_dec (n : nat) (x : X) (xs : Vector.t X n) { struct xs } : bool :=
match xs with
| [| |] => false
| y ::: xs' => if Dec (x = y) then true else in_dec x xs'
end.
Global Instance In_dec (n : nat) (x : X) (xs : Vector.t X n) : dec (In x xs).

Lemma vect_nth_In' (v : Vector.t A n) (x : A) :
Vector.In x v -> exists i : Fin.t n, Vector.nth v i = x.