(** ** Gcd *)
Definition divide x y := exists z, y=z*x.
Notation "( x | y )" := (divide x y) (at level 0) : nat_scope.

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).