Proof with auto with typeclass_instances.
intros m x.
apply relative_error_lt_conversion...
apply bpow_gt_0.
now apply relative_error_F2R_emin.
Qed.

Theorem relative_error_round :
(0 < p)%Z ->
forall x,
(bpow emin <= Rabs x)%R ->
(Rabs (round beta fexp rnd x - x) < bpow (-p + 1) * Rabs (round beta fexp rnd x))%R.