proposition: Lemma topologygenerated_imply : ∏ x : X, isfilter_imply (topologygenerated x).
proof: Proof. intros x A B H. apply hinhfun. intros L. exists (pr1 L). repeat split. - exact (pr1 (pr2 L)). - exact (pr1 (pr2 (pr2 L))). - intros y Hy. apply H, (pr2 (pr2 (pr2 L))), Hy. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures