(* 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.

Lemma BDDvar_ordered_low_1 :
forall (cfg : BDDconfig) (node1 node2 : ad),
BDDconfig_OK cfg ->
is_internal_node cfg node1 ->
is_internal_node cfg node2 ->
is_internal_node cfg (low cfg node1) \/ is_internal_node cfg (low cfg node2) ->
BDDcompare (BDDvar_max (var cfg (low cfg node1)) (var cfg (low cfg node2)))
(BDDvar_max (var cfg node1) (var cfg node2)) = Datatypes.Lt.