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.

Lemma Complement_Empty_set: forall A, Same_set (Complement A (Empty_set _)) (Full_set _).