(** 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 *)

(** ** Correctness proofs for Trunc division *)
Lemma pos_div_eucl_eq a b : 0 < b ->
let (q, r) := pos_div_eucl a b in pos a = q * b + r.