(** The helper functions are morphisms. *)

(* Specifications: *)
Lemma nu_equals : forall r r', r =R= r' -> nu r = nu r'.
Add Parametric Morphism : nu with
signature re_eq ==> bool_eq as nu_morphism.
Lemma derive_equals : forall r r', r =R= r' -> (forall a, r / a =R= r' / a).
Lemma derive_equals_inv : forall r r',
(forall a, (r / a) =R= (r' / a)) -> nu r = nu r' -> r =R= r'.