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

Theorem bezout_exists : forall (a b:nat),{u:nat & {v:nat | (is_gcd (a*u-b*v) a b)}}+{u:nat & {v:nat | (is_gcd (b*v-a*u) a b)}}.