Definition BDDalloc (cfg : BDDconfig) (x : BDDvar)
(l r : ad) :=
match cfg with
| (bs, (share, counter)) =>
let share' := BDDshare_put share x l r counter in
let bs' := MapPut _ bs counter (x, (l, r)) in
let counter' := ad_S counter in (bs', (share', counter'), counter)
end.

Lemma BDDsharing_lookup_semantics :
forall (bs : BDDstate) (share : BDDsharing_map) (n l r : ad) (x : BDDvar),
BDDsharing_OK bs share ->
(BDDshare_lookup share x l r = Some n <->
MapGet _ bs n = Some (x, (l, r))).