Inductive Set_Sum (D : Ensemble (Ensemble U)) : U -> Prop :=
    Set_Sum_intro :
      forall B : Ensemble U,
      In (Ensemble U) D B -> forall x : U, In U B x -> Set_Sum D x.Inductive Set_Sum (D : Ensemble (Ensemble U)) : U -> Prop :=
    Set_Sum_intro :
      forall B : Ensemble U,
      In (Ensemble U) D B -> forall x : U, In U B x -> Set_Sum D x.

(* Specifications: *)
Lemma Set_Sum_is_majoring : forall (D : Ensemble (Ensemble U)) (A : Ensemble U), (forall C : Ensemble U, D C -> Included U C A) -> Included U (Set_Sum D) A.
Lemma Set_Sum_is_minoring : forall (D : Ensemble (Ensemble U)) (A : Ensemble U), In (Ensemble U) D A -> Included U A (Set_Sum D).