(** The order tactic enriched with some knowledge of 0,1,2 *)

(** Decidability of equality, even though true in each finite ring, does not have a uniform proof. Otherwise, the proof for two fixed numbers would reduce to a normal form that will say if the numbers are equal or not, which cannot be true in all finite rings. Therefore, we prove decidability in the presence of order. *)
Theorem eq_decidable : forall n m, decidable (n == m).