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.
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.