proposition: Lemma ex_filter_lim_base_correct {T : TopologicalSpace} (F : Filter T) : ex_filter_lim_base F <-> ex_filter_lim F.
proof: Proof. split. - apply hinhfun. intros x. exists (pr1 x). eapply is_filter_lim_base_correct. exact (pr2 (pr2 x)). - apply hinhfun. intros x. exists (pr1 x), (base_of_neighborhood_default (pr1 x)). apply (pr2 (is_filter_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