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.

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