Proof with auto with typeclass_instances.
intros Hm x y Hx Hxy.
destruct Hx as [Hx|Hx].
rewrite ulp_neq_0.
rewrite ulp_neq_0.
apply bpow_le.
apply Hm.
now apply ln_beta_le.
apply Rgt_not_eq, Rlt_gt.
now apply Rlt_le_trans with (1:=Hx).
now apply Rgt_not_eq.
rewrite <- Hx.
apply ulp_ge_ulp_0.
apply monotone_exp_not_FTZ...
Qed.

Theorem ulp_le :
forall { Hm : Monotone_exp fexp },
forall x y: R,
(Rabs x <= Rabs y)%R ->
(ulp x <= ulp y)%R.