(** *** Multiplicative operators *)
(** Inverse *)

(* Specifications: *)
Lemma filterlim_Rbar_inv :
forall l : Rbar, l <> 0 ->
filterlim Rinv (Rbar_locally l) (Rbar_locally (Rbar_inv l)).
Lemma is_lim_seq_inv (u : nat -> R) (l : Rbar) :
is_lim_seq u l -> l <> 0 ->
is_lim_seq (fun n => / u n) (Rbar_inv l).
Lemma ex_lim_seq_inv (u : nat -> R) :
ex_lim_seq u
-> Lim_seq u <> 0
-> ex_lim_seq (fun n => / u n).
Lemma Lim_seq_inv (u : nat -> R) :
ex_lim_seq u -> (Lim_seq u <> 0)
-> Lim_seq (fun n => / u n) = Rbar_inv (Lim_seq u).