intros.
unfold is_cd.
split;try tauto.
split;apply divides_refl.
Qed.

(** two trivial lemmas: gcd(a,b) | a *)
Lemma gcd_div_l : forall (d a b:nat),(is_gcd d a b)->(divides a d).
unfold is_gcd;unfold is_cd;intros;tauto.