intros.
elim
(gcd_unicity_apart_unities Z IdZ addZ multZ OZ IZ oppZ
Z_unitary_commutative_ring integrityZ a b d1 d2 H H0).
intros.
elim (inversibleZ x); intros.
left. elim H1; intros; elim H4; intros. rewrite H6. rewrite H2.
exact (mult_IZ d1).
right. elim H1; intros; elim H4; intros. rewrite H6. rewrite H2.
simpl in |- *; exact (mult_mIZ d1).
elim H1; intros; exact H2.
Qed.

(* Specifications: *)
(***********)
Lemma gcd_OZ_absZ : forall b : Z, is_gcd Z IdZ multZ OZ OZ b (absZ b).
intros. elim (abs_eq_or_oppZ b); intro y.