(* 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 augment (vb : var_binding) (x : BDDvar)
(b : bool) (y : BDDvar) := if BDDvar_eq x y then b else vb y.
Definition bool_fun_restrict (bf : bool_fun) (x : BDDvar)
(b : bool) (vb : var_binding) := bool_fun_eval bf (augment vb x b).
Definition var_binding_eq (vb vb' : var_binding) :=
forall x : BDDvar, vb x = vb' x.
Definition bool_fun_ext (bf : bool_fun) :=
forall vb vb' : var_binding,
var_binding_eq vb vb' -> bool_fun_eval bf vb = bool_fun_eval bf vb'.
Definition bool_fun_independent (bf : bool_fun) (x : BDDvar) :=
forall vb : var_binding,
bool_fun_eval bf (augment vb x true) =
bool_fun_eval bf (augment vb x false).

Lemma bool_fun_eq_lemma :
forall (bf1 bf2 : bool_fun) (x : BDDvar),
bool_fun_ext bf1 ->
bool_fun_ext bf2 ->
bool_fun_eq (bool_fun_restrict bf1 x true) (bool_fun_restrict bf2 x true) ->
bool_fun_eq (bool_fun_restrict bf1 x false) (bool_fun_restrict bf2 x false) ->
bool_fun_eq bf1 bf2.