Proof with auto with typeclass_instances.
intros x Hd.
rewrite 2!ulp_neq_0.
now rewrite canonic_exp_DN with (2 := Hd).
intros T; contradict Hd; rewrite T, round_0...
apply Rlt_irrefl.
now apply Rgt_not_eq.
Qed.

(* Specifications: *)
Theorem round_neq_0_negligible_exp:
negligible_exp=None -> forall rnd { Zrnd : Valid_rnd rnd } x,
(x <> 0)%R ->  (round beta fexp rnd x <> 0)%R.