Definition binary_float_of_bits x :=
  FF2B prec emax _ (binary_float_of_bits_aux_correct x).

(* Specifications: *)
Theorem binary_float_of_bits_of_binary_float : forall x, binary_float_of_bits (bits_of_binary_float x) = x.
Theorem bits_of_binary_float_of_bits : forall x, (0 <= x < 2^(mw+ew+1))%Z -> bits_of_binary_float (binary_float_of_bits x) = x.