Definition CoPrime (a b : nat) := gcd (Z_of_nat a) (Z_of_nat b) 1.

Lemma gcd_lincomb_nat_dec : forall x y d : nat, x > 0 -> gcd (Z_of_nat x) (Z_of_nat y) d -> {a : Z * Z | Z_of_nat d = (Z_of_nat x * fst a + Z_of_nat y * snd a)%Z}.