(** We can now derive all properties of basic functions and orders, and use these properties for proving the specs of more advanced functions. *)
Include ZBasicProp <+ UsualMinMaxLogicalProperties <+ UsualMinMaxDecProperties.
Register eq_decidable as num.Z.eq_decidable.
Register le_decidable as num.Z.le_decidable.
Register lt_decidable as num.Z.lt_decidable.
(** ** Specification of absolute value *)

Lemma mod_pos_bound a b : 0 < b -> 0 <= a mod b < b.
Definition mod_bound_pos a b (_:0<=a) := mod_pos_bound a b.