Proof with auto with typeclass_instances.
intros Hp m x.
destruct (Req_dec x 0) as [Hx|Hx].
(* . *)
rewrite Hx, round_0...
unfold Rminus.
rewrite Rplus_0_l, Rabs_Ropp, Rabs_R0.
rewrite Rmult_0_r.
apply Rle_refl.
(* . *)
apply relative_error_N_round with (1 := Hp).
unfold x.
rewrite <- F2R_Zabs.
apply bpow_le_F2R.
apply F2R_lt_reg with beta emin.
rewrite F2R_0, F2R_Zabs.
now apply Rabs_pos_lt.
Qed.
End Fprop_relative_generic.
Section Fprop_relative_FLT.
Variable emin prec : Z.
Variable Hp : Zlt 0 prec.

Lemma relative_error_FLT_aux :
forall k, (emin + prec - 1 < k)%Z -> (prec <= k - FLT_exp emin prec k)%Z.