Module N:=DecidableEqDep(M).
(** Invariance by Substitution of Reflexive Equality Proofs *)
Proof eq_rect_eq_dec eq_dec.
(** Injectivity of Dependent Equality *)

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