(** If [a] divides [b] and [b] divides [a] then [a] is [b] or [-b]. *)

(* Specifications: *)
Lemma divide_antisym : forall a b : Z, (a | b) -> (b | a) -> a = b \/ a = - b.
(** If [a] divides [b] and [b<>0] then [|a| <= |b|]. *)
Lemma Zabs_ind :
forall (P : Z -> Prop) (x : Z),
(x >= 0 -> P x) -> (x <= 0 -> P (- x)) -> P (Zabs x).
Lemma divide_bounds : forall a b : Z, (a | b) -> b <> 0 -> Zabs a <= Zabs b.