(** d is a common divisor of a and b if d | a and d | b *)
Definition is_cd (d a b : nat) := (divides a d)/\(divides b d).(** d is a greatest common divisor of a and b if it is a maximal common divisor *)
Definition is_gcd (d a b:nat) := (is_cd d a b)/\(forall (d':nat),(is_cd d' a b)->(divides d d')).

Lemma gcd_zero : forall (a:nat),(is_gcd a O a).