(** Injectivity of equality on dependent pairs with second component
      in [Type] *)

  Notation inj_pairT2 := inj_pair2.

Lemma inj_pair2_eq_dec : forall A:Type, (forall x y:A, {x=y}+{x<>y}) -> ( forall (P:A -> Type) (p:A) (x y:P p), existT P p x = existT P p y -> x = y ).