proposition: Lemma is_lim_div (f g : R -> R) (x lf lg : Rbar) : is_lim f x lf -> is_lim g x lg -> lg <> 0 -> ex_Rbar_div lf lg -> is_lim (fun y => f y / g y) x (Rbar_div lf lg).
proof: Proof. move => Hf Hg Hlg Hl. apply is_lim_mult ; try assumption. now apply is_lim_inv. Qed.
imports: Coq(Reals ssreflect) Rcomplements Rbar Hierarchy Compactness Lim_seq