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(* 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.             *)
(*                                                                    *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
Require Export DistributedReferenceCounting.machine4.invariant5.
Require Export DistributedReferenceCounting.machine4.invariant7.
Unset Standard Proposition Elimination Names.
(* changes: In safety1 and safety2, I had to use sigma_but_strictly_positive, instead of sigma_strictly_positive.  In safety2, the case ~s2=owner should not be isolated *)

(* Specifications: *)
Lemma direct_son_is_positive :
forall c : Config,
legal c ->
forall s : Site,
direct_son c s ->
(Int (rt c s) + reduce Message dec_count (bm c s owner) +
reduce Message copy_count (bm c owner s) -
reduce Message new_inc_count (bm c s owner) > 0)%Z.