(*********************************************************)
(** *    Fractional part                                 *)
(*********************************************************)

(**********)
Definition Int_part (r:R) : Z := (up r - 1)%Z.(**********)
Definition frac_part (r:R) : R := r - IZR (Int_part r).

Lemma Int_part_INR : forall n:nat, Int_part (INR n) = Z.of_nat n.