Notation piE := (@equal_toE _ _).Canonical equal_to_pi T (qT : quotType T) (x : T) :=
  @EqualTo _ (\pi_qT x) (\pi x) (erefl _).

(* Specifications: *)
Lemma pi_morph1 : \pi (f a) = fq (equal_val x).
Lemma pi_morph2 : \pi (g a b) = gq (equal_val x) (equal_val y).
Lemma pi_mono1 : p a = pq (equal_val x).
Lemma pi_mono2 : r a b = rq (equal_val x) (equal_val y).
Lemma pi_morph11 : \pi (h a) = hq (equal_val x).