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}.