(** Compatibility results. *)

(* Specifications: *)
Lemma div_plus_compat :
forall a b c : nat, Divides a b -> Divides a c -> Divides a (b + c).
Lemma div_minus_compat :
forall a b d : nat, Divides d a -> Divides d b -> Divides d (a - b).
Lemma div_mult_compat_l :
forall a b c : nat, Divides a b -> Divides a (b * c).
Lemma div_absexp_compat :
forall (b : Z) (d : nat),
Divides d (Zabs_nat b) -> forall n : nat, Divides d (Zabs_nat (Exp b (S n))).
Lemma div_plus_r :
forall a b d : nat, Divides d a -> Divides d (a + b) -> Divides d b.