proposition: Lemma nbhs_subspace_nbhs (p : subspace A) B : nbhs p B -> nbhs p (nbhs^~ B).
proof: Proof. case: nbhs_subspaceP => [|] Ap. by move=> /nbhs_interior; apply: filterS => y A0y Ay; case: nbhs_subspaceP. by move=> E x ->; case: nbhs_subspaceP. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed