(* 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                                                     *)
Definition BDDimpl (cfg : BDDconfig) (negm : BDDneg_memo)
(orm : BDDor_memo) (node1 node2 : ad) :=
match BDDneg cfg negm node1 with
| (cfg', (node1', negm')) =>
match BDDor cfg' orm node1' node2 with
| (cfg'', (node, orm')) => (cfg'', (node, (negm', orm')))
end
end.
Definition bool_fun_impl (bf1 bf2 : bool_fun) : bool_fun :=
fun vb : var_binding => implb (bf1 vb) (bf2 vb).
Definition BDDiff (cfg : BDDconfig) (negm : BDDneg_memo)
(orm : BDDor_memo) (node1 node2 : ad) :=
match BDDimpl cfg negm orm node1 node2 with
| (cfg', (node1', (negm', orm'))) =>
match BDDimpl cfg' negm' orm' node2 node1 with
| (cfg'', (node2', (negm'', orm''))) =>
BDDand cfg'' negm'' orm'' node1' node2'
end
end.
Definition bool_fun_iff (bf1 bf2 : bool_fun) : bool_fun :=
fun vb : var_binding => eqb (bf1 vb) (bf2 vb).

Lemma BDDiff_is_iff :
forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo)
(node1 node2 : ad),
BDDconfig_OK cfg ->
BDDneg_memo_OK_2 cfg negm ->
BDDor_memo_OK cfg orm ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
bool_fun_eq
(bool_fun_of_BDD (fst (BDDiff cfg negm orm node1 node2))
(fst (snd (BDDiff cfg negm orm node1 node2))))
(bool_fun_iff (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2)).