Section Axioms.
Variable U:Type.
(** Invariance by Substitution of Reflexive Equality Proofs *)
Proof M.eq_rect_eq U.
Proof (fun p Q => M.eq_rect_eq U p Q).
(** Injectivity of Dependent Equality *)

Lemma eq_dep_eq : forall (P:U->Type) (p:U) (x y:P p), eq_dep p x p y -> x = y.