Proof with auto with typeclass_instances.
intros Y; apply generic_format_bpow.
apply valid_exp.
apply ln_beta_generic_gt...
now apply Rgt_not_eq.
now apply generic_format_canonic.
Qed.

(* Specifications: *)
Lemma d_le_m: (F2R d <= m)%R.
Lemma m_le_u: (m <= F2R u)%R.
Lemma ln_beta_m: (0 < F2R d)%R -> (ln_beta beta m =ln_beta beta (F2R d) :>Z).
Proof with auto with typeclass_instances.