Proof (fun U => eq_dep_eq__inj_pair2 U (eq_dep_eq U)).
Notation inj_pairT2 := inj_pair2.
End EqdepTheory.
(** Basic facts about eq_dep *)

Lemma f_eq_dep_non_dep :
forall U (P:U->Type) R p q x y (f:forall p, P p -> R),
eq_dep p x q y -> f p x = f q y.