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 bool_fun_independent_lemma :
forall (bf : bool_fun) (x : BDDvar) (vb : var_binding) (b : bool),
bool_fun_ext bf ->
bool_fun_independent bf x ->
bool_fun_eval bf (augment vb x b) = bool_fun_eval bf vb.