Notation bpow e := (bpow beta e).(* floating-point format with gradual underflow *)
Definition FLT_format (x : R) :=
  exists f : float beta,
  x = F2R f /\ (Zabs (Fnum f) < Zpower beta prec)%Z /\ (emin <= Fexp f)%Z.Definition FLT_exp e := Zmax (e - prec) emin.(** Properties of the FLT format *)
Global Instance FLT_exp_valid : Valid_exp FLT_exp.

Theorem generic_format_FLT_FLX : forall x : R, (bpow (emin + prec - 1) <= Rabs x)%R -> generic_format beta (FLX_exp prec) x -> generic_format beta FLT_exp x.