Definition BDDor_memo := Map (Map ad).
Definition initBDDor_memo := newMap (Map ad).
Definition BDDor_memo_put (memo : BDDor_memo) (node1 node2 node : ad) :=
let m1 :=
match MapGet _ memo node1 with
| Some y => y
| None => newMap ad
end in
let m1' := MapPut _ m1 node2 node in MapPut _ memo node1 m1'.
Definition BDDor_memo_lookup (memo : BDDor_memo) (node1 node2 : ad) :=
match MapGet _ memo node1 with
| None => None
| Some m1 =>
match MapGet _ m1 node2 with
| None => None
| Some node => Some node
end
end.
Definition BDDor_memo_OK (cfg : BDDconfig) (memo : BDDor_memo) :=
forall node1 node2 node : ad,
BDDor_memo_lookup memo node1 node2 = Some node ->
config_node_OK cfg node1 /\
config_node_OK cfg node2 /\
config_node_OK cfg node /\
BDDvar_le (var cfg node) (BDDvar_max (var cfg node1) (var cfg node2)) =
true /\
bool_fun_eq (bool_fun_of_BDD cfg node)
(bool_fun_or (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2)).

Lemma BDDor_memo_lookup_semantics :
forall (memo : BDDor_memo) (node1 node2 node node1' node2' : ad),
BDDor_memo_lookup (BDDor_memo_put memo node1 node2 node) node1' node2' =
(if Neqb node1 node1' && Neqb node2 node2'
then Some node
else BDDor_memo_lookup memo node1' node2').