proposition: Lemma ex_lim_base_correct {X : UU} {T : TopologicalSpace} (f : X → T) (F : Filter X) : ex_lim_base f F <-> ex_lim f F.
proof: Proof. split. - apply hinhfun. intros x. exists (pr1 x). eapply is_lim_base_correct. exact (pr2 (pr2 x)). - apply hinhfun. intros x. exists (pr1 x), (base_of_neighborhood_default (pr1 x)). apply (pr2 (is_lim_base_correct _ _ _ _)). exact (pr2 x). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures