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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___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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: Gt.v,v 1.8.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
35 include "Arith/Le.ma".
37 include "Arith/Lt.ma".
39 include "Arith/Plus.ma".
42 Open Local Scope nat_scope.
46 Implicit Types m n p : nat.
49 (*#* Order and successor *)
51 inline procedural "cic:/Coq/Arith/Gt/gt_Sn_O.con" as theorem.
54 Hint Resolve gt_Sn_O: arith v62.
57 inline procedural "cic:/Coq/Arith/Gt/gt_Sn_n.con" as theorem.
60 Hint Resolve gt_Sn_n: arith v62.
63 inline procedural "cic:/Coq/Arith/Gt/gt_n_S.con" as theorem.
66 Hint Resolve gt_n_S: arith v62.
69 inline procedural "cic:/Coq/Arith/Gt/gt_S_n.con" as lemma.
72 Hint Immediate gt_S_n: arith v62.
75 inline procedural "cic:/Coq/Arith/Gt/gt_S.con" as theorem.
77 inline procedural "cic:/Coq/Arith/Gt/gt_pred.con" as lemma.
80 Hint Immediate gt_pred: arith v62.
85 inline procedural "cic:/Coq/Arith/Gt/gt_irrefl.con" as lemma.
88 Hint Resolve gt_irrefl: arith v62.
93 inline procedural "cic:/Coq/Arith/Gt/gt_asym.con" as lemma.
96 Hint Resolve gt_asym: arith v62.
99 (*#* Relating strict and large orders *)
101 inline procedural "cic:/Coq/Arith/Gt/le_not_gt.con" as lemma.
104 Hint Resolve le_not_gt: arith v62.
107 inline procedural "cic:/Coq/Arith/Gt/gt_not_le.con" as lemma.
110 Hint Resolve gt_not_le: arith v62.
113 inline procedural "cic:/Coq/Arith/Gt/le_S_gt.con" as theorem.
116 Hint Immediate le_S_gt: arith v62.
119 inline procedural "cic:/Coq/Arith/Gt/gt_S_le.con" as lemma.
122 Hint Immediate gt_S_le: arith v62.
125 inline procedural "cic:/Coq/Arith/Gt/gt_le_S.con" as lemma.
128 Hint Resolve gt_le_S: arith v62.
131 inline procedural "cic:/Coq/Arith/Gt/le_gt_S.con" as lemma.
134 Hint Resolve le_gt_S: arith v62.
139 inline procedural "cic:/Coq/Arith/Gt/le_gt_trans.con" as theorem.
141 inline procedural "cic:/Coq/Arith/Gt/gt_le_trans.con" as theorem.
143 inline procedural "cic:/Coq/Arith/Gt/gt_trans.con" as lemma.
145 inline procedural "cic:/Coq/Arith/Gt/gt_trans_S.con" as theorem.
148 Hint Resolve gt_trans_S le_gt_trans gt_le_trans: arith v62.
151 (*#* Comparison to 0 *)
153 inline procedural "cic:/Coq/Arith/Gt/gt_O_eq.con" as theorem.
155 (*#* Simplification and compatibility *)
157 inline procedural "cic:/Coq/Arith/Gt/plus_gt_reg_l.con" as lemma.
159 inline procedural "cic:/Coq/Arith/Gt/plus_gt_compat_l.con" as lemma.
162 Hint Resolve plus_gt_compat_l: arith v62.