(** * Inverse function *)

(* Specifications: *)
Lemma filterlim_Rinv_0_right :
filterlim Rinv (at_right 0) (Rbar_locally p_infty).
Lemma is_lim_Rinv_0_right (f : R -> R) (x : Rbar) :
is_lim f x 0 -> Rbar_locally' x (fun x => 0 < f x) ->
is_lim (fun x => / (f x)) x p_infty.
Lemma filterlim_Rinv_0_left :
filterlim Rinv (at_left 0) (Rbar_locally m_infty).
Lemma is_lim_Rinv_0_left (f : R -> R) (x : Rbar) :
is_lim f x 0 -> Rbar_locally' x (fun x => f x < 0) ->
is_lim (fun x => / (f x)) x m_infty.