(** a and b are relatively prime if gcd(a,b)=1 *)
Definition rel_prime (a b:nat) := (is_gcd 1 a b).

Theorem bezout_rel_prime : forall (a b:nat),(rel_prime a b)<->(exists u:nat, exists v:nat, 1=a*u-b*v \/ 1 = b*v-a*u).