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

Lemma Even_Odd_div2 n :
(Even n <-> div2 n = div2 (S n)) /\ (Odd n <-> S (div2 n) = div2 (S n)).