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(* as published by the Free Software Foundation; either version 2.1   *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)

Lemma BDDdummy_lemma_2 :
forall bound : nat,
(forall m : nat,
m < bound ->
forall (cfg : BDDconfig) (node1 node2 : ad) (memo : BDDor_memo),
BDDconfig_OK cfg ->
BDDor_memo_OK cfg memo ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
(is_internal_node cfg node1 ->
is_internal_node cfg node2 ->
max (nat_of_N (var cfg node1)) (nat_of_N (var cfg node2)) < m) ->
BDDconfig_OK (fst (BDDor_1 cfg memo node1 node2 m)) /\
BDDor_memo_OK (fst (BDDor_1 cfg memo node1 node2 m))
(snd (snd (BDDor_1 cfg memo node1 node2 m))) /\
config_node_OK (fst (BDDor_1 cfg memo node1 node2 m))
(fst (snd (BDDor_1 cfg memo node1 node2 m))) /\
nodes_preserved cfg (fst (BDDor_1 cfg memo node1 node2 m)) /\
BDDvar_le
(var (fst (BDDor_1 cfg memo node1 node2 m))
(fst (snd (BDDor_1 cfg memo node1 node2 m))))
(BDDvar_max (var cfg node1) (var cfg node2)) = true /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDor_1 cfg memo node1 node2 m))
(fst (snd (BDDor_1 cfg memo node1 node2 m))))
(bool_fun_or (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2))) ->
forall (cfg : BDDconfig) (node1 node2 : ad) (memo : BDDor_memo),
BDDconfig_OK cfg ->
BDDor_memo_OK cfg memo ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
(is_internal_node cfg node1 ->
is_internal_node cfg node2 ->
max (nat_of_N (var cfg node1)) (nat_of_N (var cfg node2)) < bound) ->
BDDor_memo_lookup memo node1 node2 = None ->
in_dom (BDDvar * (ad * ad)) node1 (fst cfg) = true ->
node2 = BDDone \/ in_dom (BDDvar * (ad * ad)) node2 (fst cfg) = true ->
is_internal_node cfg node1 ->
in_dom (BDDvar * (ad * ad)) node2 (fst cfg) = true ->
is_internal_node cfg node2 ->
forall bound' : nat,
bound = S bound' ->
max (nat_of_N (var cfg node1)) (nat_of_N (var cfg node2)) < bound ->
BDDcompare (var cfg node1) (var cfg node2) = Datatypes.Eq ->
BDDconfig_OK (fst (BDDor_1 cfg memo node1 node2 bound)) /\
BDDor_memo_OK (fst (BDDor_1 cfg memo node1 node2 bound))
(snd (snd (BDDor_1 cfg memo node1 node2 bound))) /\
config_node_OK (fst (BDDor_1 cfg memo node1 node2 bound))
(fst (snd (BDDor_1 cfg memo node1 node2 bound))) /\
nodes_preserved cfg (fst (BDDor_1 cfg memo node1 node2 bound)) /\
BDDvar_le
(var (fst (BDDor_1 cfg memo node1 node2 bound))
(fst (snd (BDDor_1 cfg memo node1 node2 bound))))
(BDDvar_max (var cfg node1) (var cfg node2)) = true /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDor_1 cfg memo node1 node2 bound))
(fst (snd (BDDor_1 cfg memo node1 node2 bound))))
(bool_fun_or (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2)).