Set Implicit Arguments.
Inductive Nth {A : Type} : list A -> nat -> A -> Prop :=
| Nth_0 : forall x l, Nth (x :: l) 0 x
| Nth_S : forall l x n y, Nth l n x -> Nth (y :: l) (S n) x.
Section nth.
Variable A : Type.

Lemma nth_error_Nth :
forall n l (x : A),
nth_error l n = Some x ->
Nth l n x.