intros.
simpl in |- *.
auto.
Qed.
(* This formalisation is heavily dependent on Loic Pottier's algebra contribution *)
(* and therefore relies heavily on the algebra Hints database as well. *)
(* We feel free to extend it: *)
Hint Resolve fin_equation: algebra.

(* Specifications: *)
Lemma fin_decidable :
forall (n : Nat) (i i' : fin n), i =' i' in _ \/ ~ i =' i' in _.