Proof eq_dep_eq__inj_pairT2 U eq_dep_eq.
(** Proof-irrelevance on subsets of decidable sets *)

(* Specifications: *)
Lemma inj_pairP2 :
forall (P:U -> Prop) (x:U) (p q:P x),
ex_intro P x p = ex_intro P x q -> p = q.