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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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(* 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 DistributedReferenceCounting.machine4.invariant6.
Unset Standard Proposition Elimination Names.
(* Minute changes - in 1, deleted n0 - in 6, added n0 in initial Intros n0->n1, n1->2 - optim1 and optim2  *)

(* Specifications: *)
Lemma parent_invariant_inductive_optim1 :
forall (c : Config) (t : class_trans c) (s1 s2 : Site)
(q : queue Message) (n : s1 <> s2)
(e : bm c s1 owner = input Message dec (input Message (inc_dec s2) q)),
legal c ->
(legal c ->
forall s : Site,
indirect_son1 c s -> exists s0 : Site, direct_son c s0 /\ ancestor c s0 s) ->
legal (transition c (redirect_inc c s1 s2 q n e)) ->
forall s : Site,
indirect_son1 (transition c (redirect_inc c s1 s2 q n e)) s ->
exists s0 : Site,
direct_son (transition c (redirect_inc c s1 s2 q n e)) s0 /\
ancestor (transition c (redirect_inc c s1 s2 q n e)) s0 s.
Lemma parent_invariant_inductive :
forall (c : Config) (t : class_trans c),
legal c ->
(legal c ->
forall s : Site,
indirect_son1 c s -> exists s1 : Site, direct_son c s1 /\ ancestor c s1 s) ->
legal (transition c t) ->
forall s : Site,
indirect_son1 (transition c t) s ->
exists s1 : Site,
direct_son (transition c t) s1 /\ ancestor (transition c t) s1 s.
Lemma parent_invariant :
forall c : Config,
legal c ->
forall s : Site,
indirect_son1 c s -> exists s1 : Site, direct_son c s1 /\ ancestor c s1 s.