Proof with auto with typeclass_instances.
intros x Hx.
apply relative_error_N with (emin + prec - 1)%Z...
apply relative_error_FLT_aux.
Qed.

(* Specifications: *)
(** 1+#&epsilon;# property in rounding to nearest in FLT *)
Theorem relative_error_N_FLT_ex :
forall x,
(bpow (emin + prec - 1) <= Rabs x)%R ->
exists eps,
(Rabs eps <= /2 * bpow (-prec + 1))%R /\ round beta (FLT_exp emin prec) (Znearest choice) x = (x * (1 + eps))%R.
(** 1+#&epsilon;# property in rounding to nearest in FLT *)
Theorem relative_error_N_FLT_ex :
forall x,
(bpow (emin + prec - 1) <= Rabs x)%R ->
exists eps,
(Rabs eps <= /2 * bpow (-prec + 1))%R /\ round beta (FLT_exp emin prec) (Znearest choice) x = (x * (1 + eps))%R.