(** Opposite *)

(* Specifications: *)
Lemma LimSup_seq_opp (u : nat -> R) :
LimSup_seq (fun n => - u n) = Rbar_opp (LimInf_seq u).
Lemma LimInf_seq_opp (u : nat -> R) :
LimInf_seq (fun n => - u n) = Rbar_opp (LimSup_seq u).
Lemma Riemann_integrable_opp : forall (f : R -> R) (a b : R),
Riemann_integrable f a b ->
Riemann_integrable (fun x => - f x) a b.
Lemma RiemannInt_opp : forall (f : R -> R) (a b : R)
(pr_f : Riemann_integrable f a b)
(pr : Riemann_integrable (fun x => - f x) a b),
RiemannInt pr = - RiemannInt pr_f.