Definition bool_fun_if (x : BDDvar) (bf bf' : bool_fun) : bool_fun :=
fun vb : var_binding => ifb (vb x) (bf vb) (bf' vb).

Lemma BDDmake_var_order :
forall (cfg : BDDconfig) (l r : ad) (x : BDDvar),
BDDconfig_OK cfg ->
config_node_OK cfg l ->
config_node_OK cfg r ->
(is_internal_node cfg l -> BDDcompare (var cfg l) x = Datatypes.Lt) ->
(is_internal_node cfg r -> BDDcompare (var cfg r) x = Datatypes.Lt) ->
BDDvar_le (var (fst (BDDmake cfg x l r)) (snd (BDDmake cfg x l r))) x = true.