(** Dependent equality is equivalent to a dependent pair of equalities *)
Set Implicit Arguments.

(* Specifications: *)
Lemma eq_sigT_sig_eq X P (x1 x2:X) H1 H2 :
existT P x1 H1 = existT P x2 H2 <-> {H:x1=x2 | rew H in H1 = H2}.
Lemma eq_rect_eq__eq_dep1_eq :
Eq_rect_eq -> forall (P:U->Type) (p:U) (x y:P p), eq_dep1 p x p y -> x = y.