Definition bool_fun_restrict (bf : bool_fun) (x : BDDvar)
(b : bool) (vb : var_binding) := bool_fun_eval bf (augment vb x b).

Lemma bool_fun_restrict_eq :
forall (bf bf' : bool_fun) (x : BDDvar) (b : bool),
bool_fun_eq bf bf' ->
bool_fun_eq (bool_fun_restrict bf x b) (bool_fun_restrict bf' x b).