- apply Rlt_le, arcsinh_lt; assumption.
- rewrite xqy; apply Rle_refl.
Qed.

(* Specifications: *)
Lemma arcsinh_0 : arcsinh 0 = 0.
unfold arcsinh; rewrite pow_ne_zero, !Rplus_0_l, sqrt_1, ln_1;
[reflexivity | discriminate].