Definition Fle_bool (x y : float) :=
  match Fcompare x y with
  | Lt => true
  | Eq => true
  | _ => false
  end.

Theorem Rlt_Fexp_eq_Zlt : forall x y : float, (x < y)%R -> Fexp x = Fexp y -> (Fnum x < Fnum y)%Z.