proposition: Lemma topologysubtype_and : ∏ x : ∑ x : T, dom x, isfilter_and (topologysubtype x).
proof: Proof. intros x A B. apply hinhfun2. intros A' B'. exists (λ x, pr1 A' x ∧ pr1 B' x). repeat split. - exact (pr1 (pr1 (pr2 A'))). - exact (pr1 (pr1 (pr2 B'))). - apply isOpen_and. + exact (pr2 (pr1 (pr2 A'))). + exact (pr2 (pr1 (pr2 B'))). - apply (pr2 (pr2 A')), (pr1 X). - apply (pr2 (pr2 B')), (pr2 X). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures