proposition: Lemma is_filter_lim_base_correct {T : TopologicalSpace} (F : Filter T) (x : T) base : is_filter_lim_base F x base <-> is_filter_lim F x.
proof: Proof. split. - intros Hx P HP. apply (pr2 (neighborhood_equiv _ base _)) in HP. apply Hx. exact HP. - intros Hx P HP. apply neighborhood_equiv in HP. apply Hx. exact HP. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures