Inductive Power_set (A : Ensemble U) : Ensemble (Ensemble U) :=
       Definition_of_Power_set :
         forall X : Ensemble U,
         Included U X A -> In (Ensemble U) (Power_set A) X.Inductive Power_set (A : Ensemble U) : Ensemble (Ensemble U) :=
       Definition_of_Power_set :
         forall X : Ensemble U,
         Included U X A -> In (Ensemble U) (Power_set A) X.

Theorem Intersection_decreases_l : forall a b : Ensemble U, Included U (Intersection U a b) a.