Definition var_binding_eq (vb vb' : var_binding) :=
forall x : BDDvar, vb x = vb' x.
Definition bool_fun_ext (bf : bool_fun) :=
forall vb vb' : var_binding,
var_binding_eq vb vb' -> bool_fun_eval bf vb = bool_fun_eval bf vb'.

Lemma bool_fun_of_BDD_ext :
forall (cfg : BDDconfig) (node : ad),
bool_fun_ext (bool_fun_of_BDD cfg node).