(** 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')).

Theorem gcd_unique : forall (d d' a b:nat),(is_gcd d a b)->(is_gcd d' a b)->d=d'.