(* 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                                                     *)
(* "two_power" and "zero_lt_pow" are copied from contribs/BORDEAUX/Additions/two_power.v to avoid Requiring the contribution *)
Fixpoint two_power (m : nat) : nat :=
match m with
| O => 1
| S n => 2 * two_power n
end.

Lemma zero_lt_pow : forall a : nat, 0 < two_power a.
Definition be_to_be_inc (f : bool_expr -> bool_expr) :=
forall be1 be2 : bool_expr, be_le be1 be2 -> be_le (f be1) (f be2).