(** unbounded floating-point format with normal mantissas *)
Definition FLXN_format (x : R) :=
  exists f : float beta,
  x = F2R f /\ (x <> R0 ->
  Zpower beta (prec - 1) <= Zabs (Fnum f) < Zpower beta prec)%Z.

Theorem ulp_FLX_le: forall x, (ulp beta FLX_exp x <= Rabs x * bpow (1-prec))%R.