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.