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

(* Specifications: *)
Theorem relative_error_N_FLT_F2R_emin :
forall m, let x := F2R (Float beta m emin) in
(Rabs (round beta (FLT_exp emin prec) (Znearest choice) x - x) <= /2 * bpow (-prec + 1) * Rabs x)%R.