intros rnd x Hx.
unfold round, scaled_mantissa.
rewrite canonic_exp_FLT_FLX ; trivial.
Qed.

(* Specifications: *)
(** Links between FLT and FIX (underflow) *)
Theorem canonic_exp_FLT_FIX :
forall x, x <> 0%R ->
(Rabs x < bpow (emin + prec))%R ->
canonic_exp beta FLT_exp x = canonic_exp beta (FIX_exp emin) x.
Theorem generic_format_FIX_FLT :
forall x : R,
generic_format beta FLT_exp x ->
generic_format beta (FIX_exp emin) x.
Theorem generic_format_FLT_FIX :
forall x : R,
(Rabs x <= bpow (emin + prec))%R ->
generic_format beta (FIX_exp emin) x ->
generic_format beta FLT_exp x.
(** Links between FLT and FIX (underflow) *)
Theorem canonic_exp_FLT_FIX :
forall x, x <> 0%R ->
(Rabs x < bpow (emin + prec))%R ->
canonic_exp beta FLT_exp x = canonic_exp beta (FIX_exp emin) x.
Theorem generic_format_FIX_FLT :
forall x : R,
generic_format beta FLT_exp x ->
generic_format beta (FIX_exp emin) x.
Theorem generic_format_FLT_FIX :
forall x : R,
(Rabs x <= bpow (emin + prec))%R ->
generic_format beta (FIX_exp emin) x ->
generic_format beta FLT_exp x.