proposition: Lemma nbhs_subspaceP_subproof x : nbhs_subspace_spec x (A x) (~ A x) (x \in A) (nbhs_subspace x).
proof: Proof. rewrite /nbhs_subspace; case:(boolP (x \in A)); rewrite ?(inE, notin_set) => xA. by rewrite (@propext (A x) True)// not_True; constructor. by rewrite (@propext (A x) False)// not_False; constructor. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed