(** *** Additive operators *)
(** Opposite *)

(* Specifications: *)
Lemma filterlim_Rbar_opp :
forall x,
filterlim Ropp (Rbar_locally x) (Rbar_locally (Rbar_opp x)).
Lemma is_lim_seq_opp (u : nat -> R) (l : Rbar) :
is_lim_seq u l <-> is_lim_seq (fun n => -u n) (Rbar_opp l).
Lemma ex_lim_seq_opp (u : nat -> R) :
ex_lim_seq u <-> ex_lim_seq (fun n => -u n).
Lemma Lim_seq_opp (u : nat -> R) :
Lim_seq (fun n => - u n) = Rbar_opp (Lim_seq u).
Lemma is_lim_opp (f : R -> R) (x l : Rbar) :
is_lim f x l -> is_lim (fun y => - f y) x (Rbar_opp l).
Lemma ex_lim_opp (f : R -> R) (x : Rbar) :
ex_lim f x -> ex_lim (fun y => - f y) x.
Lemma Lim_opp (f : R -> R) (x : Rbar) :
Lim (fun y => - f y) x = Rbar_opp (Lim f x).