proposition: Lemma topologydirprod_point : ∏ (x : U × V) (P : U × V → hProp), topologydirprod x P → P x.
proof: Proof. intros xy A. apply hinhuniv. intros A'. apply (pr2 (pr2 (pr2 (pr2 A')))). - exact (pr1 (pr1 (pr2 (pr2 A')))). - exact (pr1 (pr1 (pr2 (pr2 (pr2 A'))))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures