Definition canonic_exp x :=
  fexp (ln_beta beta x).Definition canonic (f : float beta) :=
  Fexp f = canonic_exp (F2R f).Definition scaled_mantissa x :=
  (x * bpow (- canonic_exp x))%R.Definition generic_format (x : R) :=
  x = F2R (Float beta (Ztrunc (scaled_mantissa x)) (canonic_exp x)).

Theorem generic_format_discrete : forall x m, let e := canonic_exp x in (F2R (Float beta m e) < x < F2R (Float beta (m + 1) e))%R -> ~ generic_format x.