(** 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_minus : forall (d a b:nat),(a <= b)->((is_gcd d a b)<->(is_gcd d a (b-a))).