Definition bool_fun_independent (bf : bool_fun) (x : BDDvar) :=
forall vb : var_binding,
bool_fun_eval bf (augment vb x true) =
bool_fun_eval bf (augment vb x false).

Lemma BDDvar_independent_high :
forall (cfg : BDDconfig) (node : ad),
BDDconfig_OK cfg ->
is_internal_node cfg node ->
bool_fun_independent (bool_fun_of_BDD cfg (high cfg node)) (var cfg node).