1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 include "Init/Prelude.ma".
21 (*#***********************************************************************)
23 (* v * The Coq Proof Assistant / The Coq Development Team *)
25 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
27 (* \VV/ **************************************************************)
29 (* // * This file is distributed under the terms of the *)
31 (* * GNU Lesser General Public License Version 2.1 *)
33 (*#***********************************************************************)
35 (*i $Id: Le.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
37 (*#* Order on natural numbers *)
40 Open Local Scope nat_scope.
44 Implicit Types m n p : nat.
49 inline procedural "cic:/Coq/Arith/Le/le_refl.con" as theorem.
53 inline procedural "cic:/Coq/Arith/Le/le_trans.con" as theorem.
56 Hint Resolve le_trans: arith v62.
59 (*#* Order, successor and predecessor *)
61 inline procedural "cic:/Coq/Arith/Le/le_n_S.con" as theorem.
63 inline procedural "cic:/Coq/Arith/Le/le_n_Sn.con" as theorem.
65 inline procedural "cic:/Coq/Arith/Le/le_O_n.con" as theorem.
68 Hint Resolve le_n_S le_n_Sn le_O_n le_n_S: arith v62.
71 inline procedural "cic:/Coq/Arith/Le/le_pred_n.con" as theorem.
74 Hint Resolve le_pred_n: arith v62.
77 inline procedural "cic:/Coq/Arith/Le/le_Sn_le.con" as theorem.
80 Hint Immediate le_Sn_le: arith v62.
83 inline procedural "cic:/Coq/Arith/Le/le_S_n.con" as theorem.
86 Hint Immediate le_S_n: arith v62.
89 inline procedural "cic:/Coq/Arith/Le/le_pred.con" as theorem.
91 (*#* Comparison to 0 *)
93 inline procedural "cic:/Coq/Arith/Le/le_Sn_O.con" as theorem.
96 Hint Resolve le_Sn_O: arith v62.
99 inline procedural "cic:/Coq/Arith/Le/le_n_O_eq.con" as theorem.
102 Hint Immediate le_n_O_eq: arith v62.
105 (*#* Negative properties *)
107 inline procedural "cic:/Coq/Arith/Le/le_Sn_n.con" as theorem.
110 Hint Resolve le_Sn_n: arith v62.
115 inline procedural "cic:/Coq/Arith/Le/le_antisym.con" as theorem.
118 Hint Immediate le_antisym: arith v62.
121 (*#* A different elimination principle for the order on natural numbers *)
123 inline procedural "cic:/Coq/Arith/Le/le_elim_rel.con" as lemma.