proposition: Lemma neighborhood_imply : ∏ (x : T) (P Q : T → hProp), (∏ y : T, P y → Q y) → neighborhood x P → neighborhood x Q.
proof: Proof. intros x P Q H. apply hinhfun. intros O. exists (pr1 O). split. - apply (pr1 (pr2 O)). - intros y Hy. apply H. apply (pr2 (pr2 O)). exact Hy. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures