(** 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 *)

(** ** Specification of square root *)
Lemma sqrtrem_spec n : 0<=n ->
let (s,r) := sqrtrem n in n = s*s + r /\ 0 <= r <= 2*s.