Definition isNeighborhood {X : UU} (B : X → (X → hProp) → hProp) := (∏ x, isfilter_imply (B x)) × (∏ x, isfilter_htrue (B x)) × (∏ x, isfilter_and (B x)) × (∏ x P, B x P → P x) × (∏ x P, B x P → ∃ Q, B x Q × ∏ y, Q y → B y P).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.DivisionRig. Require Import UniMath.Algebra.ConstructiveStructures. Section TopologyFromNeighborhood. End TopologyFromNeighborhood. Definition TopologyFromNeighborhood {X : hSet} Lemma TopologyFromNeighborhood_correct {X : hSet} N x P <-> neighborhood (T := TopologyFromNeighborhood N H) x P. simple refine (TopologyFromNeighborhood _ _). apply TopologyFromNeighborhood_correct. simple refine (TopologyFromNeighborhood _ _). apply TopologyFromNeighborhood_correct. simple refine (TopologyFromNeighborhood _ _).