(***********************************)
(********* Intersection  ***********)
(***********************************)
(******** little intersection *******)
Definition intersection (A B : Ens) := Set_Of A (fun X : Ens => IN X B).

(* Specifications: *)
Theorem intersection_th1 : forall A B : Ens, SUB (intersection A B) A.
Proof
fun (A B U : Ens) (i : IN U (intersection A B)) =>
Set_Of_th3 A (fun X : Ens => IN X B) U i.
Theorem intersection_th2 : forall A B : Ens, SUB (intersection A B) B.
Proof
fun (A B U : Ens) (i : IN U (intersection A B)) =>
Set_Of_th2 A (fun X : Ens => IN X B) U i.
Theorem intersection_th3 :
forall (A B X : Ens) (i : IN X A) (j : IN X B), IN X (intersection A B).