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'.

(* Specifications: *)
Lemma bool_fun_of_BDD_1_ext : forall (bound : nat) (cfg : BDDconfig) (node : ad), bool_fun_ext (bool_fun_of_BDD_1 cfg node bound).
Lemma bool_fun_of_BDD_ext : forall (cfg : BDDconfig) (node : ad), bool_fun_ext (bool_fun_of_BDD cfg node).
Lemma augment_eq : forall (vb : var_binding) (x : BDDvar) (b : bool), vb x = b -> var_binding_eq (augment vb x b) vb.