Section Set_Sums.
Variable U : Type.
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.

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.