Add Parametric Relation {A} : (Ensemble A) Same_set
    reflexivity proved by (Same_set_refl A)
    symmetry proved by (Same_set_sym A)
    transitivity proved by (Same_set_trans A) as Same_set_rel.

(* Specifications: *)
Lemma Same_set_spec: forall A P Q, Same_set P Q <-> (pointwise_relation A iff) P Q.
Lemma Complement_Empty_set: forall A, Same_set (Complement A (Empty_set _)) (Full_set _).
Lemma Intersection_comm: forall A P Q, Same_set (Intersection A P Q) (Intersection A Q P).
Lemma Intersection_assoc: forall A P Q R, Same_set (Intersection A (Intersection A P Q) R) (Intersection A P (Intersection A Q R)).
Lemma Union_comm: forall A P Q, Same_set (Union A P Q) (Union A Q P).
Lemma Union_assoc: forall A P Q R, Same_set (Union A (Union A P Q) R) (Union A P (Union A Q R)).
Lemma Intersection_Union_distr_l: forall A P Q R, Same_set (Intersection A (Union A Q R) P) (Union A (Intersection A Q P) (Intersection A R P)).
Lemma Intersection_Union_distr_r: forall A P Q R, Same_set (Intersection A P (Union A Q R)) (Union A (Intersection A P Q) (Intersection A P R)).