proposition: Lemma Lim_div (f g : R -> R) (x : Rbar) : ex_lim f x -> ex_lim g x -> Lim g x <> 0 -> ex_Rbar_div (Lim f x) (Lim g x) -> Lim (fun y => f y / g y) x = Rbar_div (Lim f x) (Lim g x).
proof: Proof. move => Hf Hg Hlg Hl. apply is_lim_unique. apply is_lim_div ; try apply Lim_correct ; assumption. Qed.
imports: Coq(Reals ssreflect) Rcomplements Rbar Hierarchy Compactness Lim_seq