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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
Section BDD_neg.
Variable gc : BDDconfig -> list ad -> BDDconfig.
Hypothesis gc_is_OK : gc_OK gc.
Fixpoint BDDneg_1 (cfg : BDDconfig) (ul : list ad)
(node : ad) (bound : nat) {struct bound} : BDDconfig * ad :=
match bound with
| O => (* Error *)  (initBDDconfig, BDDzero)
| S bound' =>
match MapGet _ (negm_of_cfg cfg) node with
| Some node' => (cfg, node')
| None =>
match MapGet _ (fst cfg) node with
| None =>
if Neqb node BDDzero
then (BDDneg_memo_put cfg BDDzero BDDone, BDDone)
else (BDDneg_memo_put cfg BDDone BDDzero, BDDzero)
| Some (x, (l, r)) =>
match BDDneg_1 cfg ul l bound' with
| (cfgl, nodel) =>
match BDDneg_1 cfgl (nodel :: ul) r bound' with
| (cfgr, noder) =>
match
BDDmake gc cfgr x nodel noder (noder :: nodel :: ul)
with
| (cfg', node') =>
(BDDneg_memo_put cfg' node node', node')
end
end
end
end
end
end.

Lemma BDDneg_1_lemma :
forall (bound : nat) (cfg : BDDconfig) (ul : list ad) (node : ad),
nat_of_N (node_height cfg node) < bound ->
BDDconfig_OK cfg ->
used_list_OK cfg ul ->
used_node' cfg ul node ->
BDDconfig_OK (fst (BDDneg_1 cfg ul node bound)) /\
config_node_OK (fst (BDDneg_1 cfg ul node bound))
(snd (BDDneg_1 cfg ul node bound)) /\
used_nodes_preserved cfg (fst (BDDneg_1 cfg ul node bound)) ul /\
Neqb
(node_height (fst (BDDneg_1 cfg ul node bound))
(snd (BDDneg_1 cfg ul node bound))) (node_height cfg node) = true /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDneg_1 cfg ul node bound))
(snd (BDDneg_1 cfg ul node bound)))
(bool_fun_neg (bool_fun_of_BDD cfg node)).