(** Definition and basic properties about the ulp *)
(** Now includes a nice ulp(0): ulp(0) is now 0 when there is no minimal exponent, such as in FLX, and beta^(fexp n) when there is a n such that n <= fexp n. For instance, the value of ulp(O) is then beta^emin in FIX and FLT. The main lemma to use is ulp_neq_0 that is equivalent to the previous "unfold ulp" provided the value is not zero. *)

(* was ulp_DN_UP *)
Theorem round_UP_DN_ulp :
forall x, ~ F x ->
round beta fexp Zceil x = (round beta fexp Zfloor x + ulp x)%R.