(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
(**************************************************************************)

(* This file was automatically generated: do not edit *********************)

include "Coq.ma".

(*i $Id: i*)

(*s Axioms for the basic numerical operations *)

include "Num/Params.ma".

include "Num/EqAxioms.ma".

include "Num/NSyntax.ma".

(*s Lemmas for [add] *)

inline procedural "cic:/Coq/Num/Nat/Axioms/add_Sx_y.con" as lemma.

(* UNEXPORTED
Hints Resolve add_Sx_y : nat.
*)

(*s Lemmas for [add] *)

inline procedural "cic:/Coq/Num/Nat/Axioms/add_0_x.con" as lemma.

(* UNEXPORTED
Hints Resolve add_0_x : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/add_sym.con" as lemma.

(* UNEXPORTED
Hints Resolve add_sym : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/add_eq_compat.con" as lemma.

(* UNEXPORTED
Hints Resolve add_eq_compat : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/add_assoc_l.con" as lemma.

(*s Lemmas for [one] *)

inline procedural "cic:/Coq/Num/Nat/Axioms/S_0_1.con" as lemma.

(*s Lemmas for [<], 
    properties of [>], [<=] and [>=] will be derived from [<] *)

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_trans.con" as lemma.

(* UNEXPORTED
Hints Resolve lt_trans : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_x_Sx.con" as lemma.

(* UNEXPORTED
Hints Resolve lt_x_Sx : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_S_compat.con" as lemma.

(* UNEXPORTED
Hints Resolve lt_S_compat : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_eq_compat.con" as lemma.

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_add_compat_l.con" as lemma.

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_Sx_Sy_lt.con" as lemma.

(* UNEXPORTED
Hints Immediate lt_Sx_Sy_lt : nat.
*)

inline procedural "cic:/Coq/Num/Nat/Axioms/lt_anti_refl.con" as lemma.