Definition Its_empty (A : Ens) := forall X : Ens, ~ IN X A.

(* Specifications: *)
Lemma ieieep1_Out : IN X EmptySet.
Lemma ieieep2_Out : IN X A.
Lemma ieieep_Out : EQ A EmptySet.
Theorem its_empty_implies_equals_emptyset : forall (A : Ens) (k : Its_empty A), EQ A EmptySet.
Theorem Its_empty_emptyset : Its_empty EmptySet.