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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
Section BDD_or.
Variable gc : BDDconfig -> list ad -> BDDconfig.
Hypothesis gc_is_OK : gc_OK gc.
Fixpoint BDDor_1 (cfg : BDDconfig) (ul : list ad) (node1 node2 : ad)
(bound : nat) {struct bound} : BDDconfig * ad :=
match bound with
| O => (* Error *)  (initBDDconfig, BDDzero)
| S bound' =>
match MapGet2 _ (orm_of_cfg cfg) node1 node2 with
| Some node' => (cfg, node')
| None =>
match MapGet _ (fst cfg) node1 with
| None =>
if Neqb node1 BDDzero
then (BDDor_memo_put cfg node1 node2 node2, node2)
else (BDDor_memo_put cfg node1 node2 node1, node1)
| Some (x1, (l1, r1)) =>
match MapGet _ (fst cfg) node2 with
| None =>
if Neqb node2 BDDzero
then (BDDor_memo_put cfg node1 node2 node1, node1)
else (BDDor_memo_put cfg node1 node2 node2, node2)
| Some (x2, (l2, r2)) =>
match BDDcompare x1 x2 with
| Datatypes.Eq =>
match BDDor_1 cfg ul l1 l2 bound' with
| (cfgl, nodel) =>
match BDDor_1 cfgl (nodel :: ul) r1 r2 bound' with
| (cfgr, noder) =>
match
BDDmake gc cfgr x1 nodel noder
(noder :: nodel :: ul)
with
| (cfg', node') =>
(BDDor_memo_put cfg' node1 node2 node',
node')
end
end
end
| Datatypes.Gt =>
match BDDor_1 cfg ul l1 node2 bound' with
| (cfgl, nodel) =>
match
BDDor_1 cfgl (nodel :: ul) r1 node2 bound'
with
| (cfgr, noder) =>
match
BDDmake gc cfgr x1 nodel noder
(noder :: nodel :: ul)
with
| (cfg', node') =>
(BDDor_memo_put cfg' node1 node2 node',
node')
end
end
end
| Datatypes.Lt =>
match BDDor_1 cfg ul node1 l2 bound' with
| (cfgl, nodel) =>
match
BDDor_1 cfgl (nodel :: ul) node1 r2 bound'
with
| (cfgr, noder) =>
match
BDDmake gc cfgr x2 nodel noder
(noder :: nodel :: ul)
with
| (cfg', node') =>
(BDDor_memo_put cfg' node1 node2 node',
node')
end
end
end
end
end
end
end
end.

Lemma BDDor_1_lemma :
forall (bound : nat) (cfg : BDDconfig) (ul : list ad) (node1 node2 : ad),
max (nat_of_N (node_height cfg node1)) (nat_of_N (node_height cfg node2)) <
bound ->
BDDconfig_OK cfg ->
used_list_OK cfg ul ->
used_node' cfg ul node1 ->
used_node' cfg ul node2 ->
BDDconfig_OK (fst (BDDor_1 cfg ul node1 node2 bound)) /\
config_node_OK (fst (BDDor_1 cfg ul node1 node2 bound))
(snd (BDDor_1 cfg ul node1 node2 bound)) /\
used_nodes_preserved cfg (fst (BDDor_1 cfg ul node1 node2 bound)) ul /\
Nleb
(node_height (fst (BDDor_1 cfg ul node1 node2 bound))
(snd (BDDor_1 cfg ul node1 node2 bound)))
(BDDvar_max (node_height cfg node1) (node_height cfg node2)) = true /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDor_1 cfg ul node1 node2 bound))
(snd (BDDor_1 cfg ul node1 node2 bound)))
(bool_fun_or (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2)).