(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Require Export reduce.
Require Export table.
Require Export abstract_machine.
Section SUM_REDUCE.
Variable Data : Set.
Variable s0 : Site.
Let Bag_of_message := Bag_of_Data Data.
Variable f : Data -> Z.
Definition sigma_reduce (bom : Bag_of_message) :=
sigma Site LS (fun si : Site => reduce Data f (bom s0 si)).

Lemma sigma_reduce_pos :
forall (s0 s1 : Site) (bom : Bag_of_message),
(forall m : Data, (f m > 0)%Z) -> (sigma_reduce bom >= 0)%Z.