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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
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Set Implicit Arguments.
(* Set Universe Polymorphism. *)
(* An object to return when an expression is not recognized as a constant *)
Definition NotConstant := false.
(** Z is a ring and a setoid*)

(* Specifications: *)
Lemma Zsth : Setoid_Theory Z (@eq Z).
Proof (Eqsth Z).
Lemma Zeqe : ring_eq_ext Z.add Z.mul Z.opp (@eq Z).
Proof (Eq_ext Z.add Z.mul Z.opp).
Lemma Zth : ring_theory Z0 (Zpos xH) Z.add Z.mul Z.sub Z.opp (@eq Z).
Section ZMORPHISM.