(** Additional results about [Even] and [Odd] *)

Definition Even_Odd_dec n : {Even n} + {Odd n}.

Lemma Even_add_aux n m : (Odd (n + m) <-> Odd n /\ Even m \/ Even n /\ Odd m) /\ (Even (n + m) <-> Even n /\ Even m \/ Odd n /\ Odd m).