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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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(* 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.                       *)
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(* 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                                                     *)
Inductive BDDdummy_type1 : Set :=
BDDdummy1 : BDDconfig * ad * BDDneg_memo -> BDDdummy_type1.
Inductive BDDdummy_type2 : Set :=
BDDdummy2 : BDDconfig * ad -> BDDdummy_type2.
Inductive BDDdummy_type3 : Set :=
BDDdummy3 : BDDconfig * (ad * BDDor_memo) -> BDDdummy_type3.
Definition initBDDneg_memo : BDDneg_memo := newMap ad.
Fixpoint BDDneg_1_1 (cfg : BDDconfig) (memo : BDDneg_memo)
(node : ad) (bound : nat) {struct bound} : BDDconfig * ad * BDDneg_memo :=
match BDDneg_memo_lookup memo node with
| Some node' => (cfg, node', memo)
| None =>
match MapGet _ (fst cfg) node with
| None =>
if Neqb node BDDzero
then (cfg, BDDone, BDDneg_memo_put memo BDDzero BDDone)
else (cfg, BDDzero, BDDneg_memo_put memo BDDone BDDzero)
| Some (x, (l, r)) =>
match bound with
| O => (initBDDconfig, BDDzero, initBDDneg_memo)
| S bound' =>
match BDDdummy1 (BDDneg_1_1 cfg memo l bound') with
| BDDdummy1 ((cfgl, nodel), memol) =>
match BDDdummy1 (BDDneg_1_1 cfgl memol r bound') with
| BDDdummy1 ((cfgr, noder), memor) =>
match BDDdummy2 (BDDmake cfgr x nodel noder) with
| BDDdummy2 (cfg', node') =>
(cfg', node', BDDneg_memo_put memor node node')
end
end
end
end
end
end.

Lemma BDDneg_1_1_eq_1 :
forall (bound : nat) (cfg : BDDconfig) (memo : BDDneg_memo) (node : ad),
BDDneg_1_1 cfg memo node bound = BDDneg_1 (cfg, node, memo) bound.