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(* -*- coding: utf-8 -*- *)
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* File Eqdep.v created by Christine Paulin-Mohring in Coq V5.6, May 1992 *)
(* Abstraction with respect to the eq_rect_eq axiom and creation of
EqdepFacts.v by Hugo Herbelin, Mar 2006 *)
(** This file axiomatizes the invariance by substitution of reflexive
equality proofs [[Streicher93]] and exports its consequences, such
as the injectivity of the projection of the dependent pair.
[[Streicher93]] T. Streicher, Semantical Investigations into
Intensional Type Theory, Habilitationsschrift, LMU München, 1993.
*)
Require Export EqdepFacts.
Module Eq_rect_eq.
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.
End Eq_rect_eq.
Module EqdepTheory := EqdepTheory(Eq_rect_eq).
Export EqdepTheory.
(** Exported hints *)
Hint Resolve eq_dep_eq: eqdep.
Hint Resolve inj_pair2 inj_pairT2: eqdep.
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