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

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.