proposition: Lemma rel_prime_bezout : forall a b, rel_prime a b -> {u : Z & {v | u * a + v * b = 1}}.
proof: Proof. intros a b RP. rewrite <- (proj2 (Zgcd_1_rel_prime a b)); auto. apply bezout_inj. Qed.
imports: ZArith Lia Znumtheory Natsets MyNat Ztools Zeqm