proposition: Lemma neighborhood_neighborhood : ∏ (x : T) (P : T → hProp), neighborhood x P → ∃ Q : T → hProp, neighborhood x Q × ∏ y : T, Q y → neighborhood y P.
proof: Proof. intros x P. apply hinhfun. intros Q. exists (pr1 Q). split. - apply (pr2 (neighborhood_isOpen _)). + apply (pr2 (pr1 Q)). + apply (pr1 (pr2 Q)). - intros y Qy. apply hinhpr. exists (pr1 Q). split. + exact Qy. + exact (pr2 (pr2 Q)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures