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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
(** Relative primality *)
Definition rel_prime (a b : Z) : Prop := gcd a b 1.
(** Bezout's theorem: [a] and [b] are relatively prime if and only if there exist [u] and [v] such that [ua+vb = 1]. *)

Lemma rel_prime_bezout : forall a b : Z, rel_prime a b -> Bezout a b 1.