Proof with auto with typeclass_instances.
intros m x.
apply relative_error_lt_conversion...
apply bpow_gt_0.
now apply relative_error_FLT_F2R_emin.
Qed.

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