(* 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 BDDvar_le := Nleb.
Definition BDDvar_max (x y : BDDvar) := if BDDvar_le x y then y else x.
Definition bool_fun_if (x : BDDvar) (bf bf' : bool_fun) : bool_fun :=
fun vb : var_binding => ifb (vb x) (bf vb) (bf' vb).

Lemma bool_fun_if_lemma_2 :
forall (cfg : BDDconfig) (node : ad),
BDDconfig_OK cfg ->
is_internal_node cfg node ->
bool_fun_eq (bool_fun_of_BDD cfg node)
(bool_fun_if (var cfg node) (bool_fun_of_BDD cfg (high cfg node))
(bool_fun_of_BDD cfg (low cfg node))).