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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (*#**********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
25 (* \VV/ *************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#**********************************************************************)
33 (*i $Id: BinNat.v,v 1.7 2003/11/29 17:28:34 herbelin Exp $ i*)
35 include "NArith/BinPos.ma".
37 (*#*********************************************************************)
39 (*#* Binary natural numbers *)
41 inline procedural "cic:/Coq/NArith/BinNat/N.ind".
43 (*#* Declare binding key for scope positive_scope *)
46 Delimit Scope N_scope with N.
49 (*#* Automatically open scope N_scope for the constructors of N *)
52 Bind Scope N_scope with N.
56 Arguments Scope Npos [N_scope].
60 Open Local Scope N_scope.
63 (*#* Operation x -> 2*x+1 *)
65 inline procedural "cic:/Coq/NArith/BinNat/Ndouble_plus_one.con" as definition.
67 (*#* Operation x -> 2*x *)
69 inline procedural "cic:/Coq/NArith/BinNat/Ndouble.con" as definition.
73 inline procedural "cic:/Coq/NArith/BinNat/Nsucc.con" as definition.
77 inline procedural "cic:/Coq/NArith/BinNat/Nplus.con" as definition.
80 Infix "+" := Nplus : N_scope.
83 (*#* Multiplication *)
85 inline procedural "cic:/Coq/NArith/BinNat/Nmult.con" as definition.
88 Infix "*" := Nmult : N_scope.
93 inline procedural "cic:/Coq/NArith/BinNat/Ncompare.con" as definition.
96 Infix "?=" := Ncompare (at level 70, no associativity) : N_scope.
99 (*#* Peano induction on binary natural numbers *)
101 inline procedural "cic:/Coq/NArith/BinNat/Nind.con" as theorem.
103 (*#* Properties of addition *)
105 inline procedural "cic:/Coq/NArith/BinNat/Nplus_0_l.con" as theorem.
107 inline procedural "cic:/Coq/NArith/BinNat/Nplus_0_r.con" as theorem.
109 inline procedural "cic:/Coq/NArith/BinNat/Nplus_comm.con" as theorem.
111 inline procedural "cic:/Coq/NArith/BinNat/Nplus_assoc.con" as theorem.
113 inline procedural "cic:/Coq/NArith/BinNat/Nplus_succ.con" as theorem.
115 inline procedural "cic:/Coq/NArith/BinNat/Nsucc_inj.con" as theorem.
117 inline procedural "cic:/Coq/NArith/BinNat/Nplus_reg_l.con" as theorem.
119 (*#* Properties of multiplication *)
121 inline procedural "cic:/Coq/NArith/BinNat/Nmult_1_l.con" as theorem.
123 inline procedural "cic:/Coq/NArith/BinNat/Nmult_1_r.con" as theorem.
125 inline procedural "cic:/Coq/NArith/BinNat/Nmult_comm.con" as theorem.
127 inline procedural "cic:/Coq/NArith/BinNat/Nmult_assoc.con" as theorem.
129 inline procedural "cic:/Coq/NArith/BinNat/Nmult_plus_distr_r.con" as theorem.
131 inline procedural "cic:/Coq/NArith/BinNat/Nmult_reg_r.con" as theorem.
133 inline procedural "cic:/Coq/NArith/BinNat/Nmult_0_l.con" as theorem.
135 (*#* Properties of comparison *)
137 inline procedural "cic:/Coq/NArith/BinNat/Ncompare_Eq_eq.con" as theorem.