Definition BDDmake (cfg : BDDconfig) (x : BDDvar) 
    (l r : ad) :=
    if Neqb l r
    then (cfg, l)
    else
     match cfg with
     | (bs, (share, counter)) =>
         match BDDshare_lookup share x l r with
         | Some y => (cfg, y)
         | None => BDDalloc cfg x l r
         end
     end.

Lemma BDDmake_semantics : forall (cfg : BDDconfig) (l r : ad) (x : BDDvar), BDDconfig_OK cfg -> node_OK (fst cfg) l -> node_OK (fst cfg) r -> (forall (xl : BDDvar) (ll rl : ad), MapGet _ (fst cfg) l = Some (xl, (ll, rl)) -> BDDcompare xl x = Datatypes.Lt) -> (forall (xr : BDDvar) (lr rr : ad), MapGet _ (fst cfg) r = Some (xr, (lr, rr)) -> BDDcompare xr x = Datatypes.Lt) -> BDDconfig_OK (fst (BDDmake cfg x l r)) /\ (Neqb l r = false -> MapGet _ (fst (fst (BDDmake cfg x l r))) (snd (BDDmake cfg x l r)) = Some (x, (l, r))) /\ (Neqb l r = true -> snd (BDDmake cfg x l r) = l) /\ (forall (a l' r' : ad) (x' : BDDvar), (MapGet _ (fst (fst (BDDmake cfg x l r))) a = Some (x', (l', r')) -> MapGet _ (fst cfg) a = Some (x', (l', r')) \/ snd (BDDmake cfg x l r) = a) /\ (MapGet _ (fst cfg) a = Some (x', (l', r')) -> MapGet _ (fst (fst (BDDmake cfg x l r))) a = Some (x', (l', r')))) /\ node_OK (fst (fst (BDDmake cfg x l r))) (snd (BDDmake cfg x l r)).