rewrite pow_O ln_1 ; simpl ; ring.
rewrite S_INR ; simpl ; rewrite ln_mult ; try intuition.
rewrite IH ; ring.
Qed.

(* Specifications: *)
Lemma ln_le x y : 0 < x -> x <= y -> ln x <= ln y.
Lemma ln_div x y : 0 < x -> 0 < y -> ln (x / y) = ln x - ln y.
(** * Other *)
Lemma derivable_pt_lim_atan :
forall x, derivable_pt_lim atan x (/(1 + x^2)).