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 augment_eq : forall (vb : var_binding) (x : BDDvar) (b : bool), vb x = b -> var_binding_eq (augment vb x b) vb.