(* Contribution to the Coq Library   V6.3 (July 1999)                       *)
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(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.11                                 *)
(*                              Feb 2nd 1996                                *)
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(*                (notations and layout updated March 2009)                 *)
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(*                                  Sum.v                                   *)
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(* This file is distributed under the terms of the                          *)
(* GNU Lesser General Public License Version 2.1                            *)
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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.