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(* 02110-1301 USA                                                     *)
(** natZ. Some lemmas about inject_nat, absolu and the relation between Z and nat in general.  @author Olga Caprotti and Martijn Oostdijk @version $Revision$ *)

Lemma abs_minus_pos :
forall x y : Z,
(0 <= x)%Z ->
(0 <= y)%Z -> (x >= y)%Z -> Z.abs_nat (x - y) = Z.abs_nat x - Z.abs_nat y.