proposition: Lemma nbhsE (p : T) : nbhs p = [set A : set T | exists2 B : set T, open_nbhs p B & B `<=` A].
proof: Proof. have -> : nbhs p = [set A : set T | exists B, [/\ open B, B p & B `<=` A] ]. exact: nbhsE_subproof. by rewrite predeqE => A; split=> [[B [?]]|[B[]]]; exists B. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed