Definition cos_n (n:nat) : R := (-1) ^ n / INR (fact (2 * n)).

(* Specifications: *)
Lemma simpl_cos_n : forall n:nat, cos_n (S n) / cos_n n = - / INR (2 * S n * (2 * n + 1)).
Lemma archimed_cor1 : forall eps:R, 0 < eps -> exists N : nat, / INR N < eps /\ (0 < N)%nat.
Lemma Alembert_cos : Un_cv (fun n:nat => Rabs (cos_n (S n) / cos_n n)) 0.
Lemma cosn_no_R0 : forall n:nat, cos_n n <> 0.