Proof (eq_rect_eq__eq_dep_eq U eq_rect_eq).
(** Uniqueness of Identity Proofs (UIP) *)

(* Specifications: *)
Lemma UIP : forall (x y:U) (p1 p2:x = y), p1 = p2.
Proof (eq_dep_eq__UIP U eq_dep_eq).
Lemma UIP : forall (x y:U) (p1 p2:x = y), p1 = p2.
Proof (eq_dep_eq__UIP U eq_dep_eq).