Definition BDDiff (cfg : BDDconfig) (negm : BDDneg_memo)
(orm : BDDor_memo) (node1 node2 : ad) :=
match BDDimpl cfg negm orm node1 node2 with
| (cfg', (node1', (negm', orm'))) =>
match BDDimpl cfg' negm' orm' node2 node1 with
| (cfg'', (node2', (negm'', orm''))) =>
BDDand cfg'' negm'' orm'' node1' node2'
end
end.

(* Specifications: *)
Lemma BDDiff_keeps_config_OK :
forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo)
(node1 node2 : ad),
BDDconfig_OK cfg ->
BDDneg_memo_OK_2 cfg negm ->
BDDor_memo_OK cfg orm ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
BDDconfig_OK (fst (BDDiff cfg negm orm node1 node2)).
Lemma BDDiff_node_OK :
forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo)
(node1 node2 : ad),
BDDconfig_OK cfg ->
BDDneg_memo_OK_2 cfg negm ->
BDDor_memo_OK cfg orm ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
config_node_OK (fst (BDDiff cfg negm orm node1 node2))
(fst (snd (BDDiff cfg negm orm node1 node2))).
Lemma BDDiff_preserves_nodes :
forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo)
(node1 node2 : ad),
BDDconfig_OK cfg ->
BDDneg_memo_OK_2 cfg negm ->
BDDor_memo_OK cfg orm ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
nodes_preserved cfg (fst (BDDiff cfg negm orm node1 node2)).
Lemma BDDiff_keeps_neg_memo_OK :
forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo)
(node1 node2 : ad),
BDDconfig_OK cfg ->
BDDneg_memo_OK_2 cfg negm ->
BDDor_memo_OK cfg orm ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
BDDneg_memo_OK_2 (fst (BDDiff cfg negm orm node1 node2))
(fst (snd (snd (BDDiff cfg negm orm node1 node2)))).
Lemma BDDiff_keeps_or_memo_OK :
forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo)
(node1 node2 : ad),
BDDconfig_OK cfg ->
BDDneg_memo_OK_2 cfg negm ->
BDDor_memo_OK cfg orm ->
config_node_OK cfg node1 ->
config_node_OK cfg node2 ->
BDDor_memo_OK (fst (BDDiff cfg negm orm node1 node2))
(snd (snd (snd (BDDiff cfg negm orm node1 node2)))).