(* 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                                                     *)

Lemma BDDneg_1_lemma' :
forall (bound : nat) (arg : BDDconfig * ad * BDDneg_memo),
BDDconfig_OK (fst (fst arg)) ->
config_node_OK (fst (fst arg)) (snd (fst arg)) ->
BDDneg_memo_OK_2 (fst (fst arg)) (snd arg) ->
(is_internal_node (fst (fst arg)) (snd (fst arg)) ->
nat_of_N (var (fst (fst arg)) (snd (fst arg))) < bound) ->
fst (BDDneg_1 arg bound) = BDDneg_2 (fst (fst arg)) (snd (fst arg)) bound /\
BDDneg_memo_OK_2 (fst (fst (BDDneg_1 arg bound))) (snd (BDDneg_1 arg bound)).