(**************************************************************************)
(*       ___                                                              *)
(*      ||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".

(*#***********************************************************************)

(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)

(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)

(*   \VV/  **************************************************************)

(*    //   *      This file is distributed under the terms of the       *)

(*         *       GNU Lesser General Public License Version 2.1        *)

(*#***********************************************************************)

(*i $Id: BinNat.v,v 1.7.2.1 2004/07/16 19:31:07 herbelin Exp $ i*)

include "NArith/BinPos.ma".

(*#*********************************************************************)

(*#* Binary natural numbers *)

inline procedural "cic:/Coq/NArith/BinNat/N.ind".

(*#* Declare binding key for scope positive_scope *)

(* UNEXPORTED
Delimit Scope N_scope with N.
*)

(*#* Automatically open scope N_scope for the constructors of N *)

(* UNEXPORTED
Bind Scope N_scope with N.
*)

(* UNEXPORTED
Arguments Scope Npos [N_scope].
*)

(* UNEXPORTED
Open Local Scope N_scope.
*)

(*#* Operation x -> 2*x+1 *)

inline procedural "cic:/Coq/NArith/BinNat/Ndouble_plus_one.con" as definition.

(*#* Operation x -> 2*x *)

inline procedural "cic:/Coq/NArith/BinNat/Ndouble.con" as definition.

(*#* Successor *)

inline procedural "cic:/Coq/NArith/BinNat/Nsucc.con" as definition.

(*#* Addition *)

inline procedural "cic:/Coq/NArith/BinNat/Nplus.con" as definition.

(* NOTATION
Infix "+" := Nplus : N_scope.
*)

(*#* Multiplication *)

inline procedural "cic:/Coq/NArith/BinNat/Nmult.con" as definition.

(* NOTATION
Infix "*" := Nmult : N_scope.
*)

(*#* Order *)

inline procedural "cic:/Coq/NArith/BinNat/Ncompare.con" as definition.

(* NOTATION
Infix "?=" := Ncompare (at level 70, no associativity) : N_scope.
*)

(*#* Peano induction on binary natural numbers *)

inline procedural "cic:/Coq/NArith/BinNat/Nind.con" as theorem.

(*#* Properties of addition *)

inline procedural "cic:/Coq/NArith/BinNat/Nplus_0_l.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nplus_0_r.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nplus_comm.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nplus_assoc.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nplus_succ.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nsucc_inj.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nplus_reg_l.con" as theorem.

(*#* Properties of multiplication *)

inline procedural "cic:/Coq/NArith/BinNat/Nmult_1_l.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nmult_1_r.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nmult_comm.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nmult_assoc.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nmult_plus_distr_r.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nmult_reg_r.con" as theorem.

inline procedural "cic:/Coq/NArith/BinNat/Nmult_0_l.con" as theorem.

(*#* Properties of comparison *)

inline procedural "cic:/Coq/NArith/BinNat/Ncompare_Eq_eq.con" as theorem.