proposition: Lemma topologysubtype_imply : ∏ x : ∑ x : T, dom x, isfilter_imply (topologysubtype x).
proof: Proof. intros x A B H. apply hinhfun. intros A'. exists (pr1 A'). split. - exact (pr1 (pr2 A')). - intros y Hy. now apply H, (pr2 (pr2 A')). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures