Proof (UIP_refl__Streicher_K U UIP_refl).
End Axioms.
(** UIP implies the injectivity of equality on dependent pairs in Type *)

(* Specifications: *)
Lemma inj_pair2 :
forall (U:Type) (P:U -> Type) (p:U) (x y:P p),
existT P p x = existT P p y -> x = y.