End Corollaries.
Notation Inj_dep_pairS := Inj_dep_pair.
Notation Inj_dep_pairT := Inj_dep_pair.
Notation eq_dep_eq__inj_pairT2 := eq_dep_eq__inj_pair2.
(************************************************************************)
(** * Definition of the functor that builds properties of dependent equalities assuming axiom eq_rect_eq *)
Module Type EqdepElimination.

(* Specifications: *)
Axiom eq_rect_eq :
forall (U:Type) (p:U) (Q:U -> Type) (x:Q p) (h:p = p),
x = eq_rect p Q x p h.