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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 *)
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19 (*#**********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
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27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
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33 (*i $Id: Max.v,v 1.7 2003/11/29 17:28:28 herbelin Exp $ i*)
35 include "Arith/Arith.ma".
38 Open Local Scope nat_scope.
42 Implicit Types m n : nat.
45 (*#* maximum of two natural numbers *)
47 inline procedural "cic:/Coq/Arith/Max/max.con" as definition.
49 (*#* Simplifications of [max] *)
51 inline procedural "cic:/Coq/Arith/Max/max_SS.con" as lemma.
53 inline procedural "cic:/Coq/Arith/Max/max_comm.con" as lemma.
55 (*#* [max] and [le] *)
57 inline procedural "cic:/Coq/Arith/Max/max_l.con" as lemma.
59 inline procedural "cic:/Coq/Arith/Max/max_r.con" as lemma.
61 inline procedural "cic:/Coq/Arith/Max/le_max_l.con" as lemma.
63 inline procedural "cic:/Coq/Arith/Max/le_max_r.con" as lemma.
66 Hint Resolve max_r max_l le_max_l le_max_r: arith v62.
69 (*#* [max n m] is equal to [n] or [m] *)
71 inline procedural "cic:/Coq/Arith/Max/max_dec.con" as lemma.
73 inline procedural "cic:/Coq/Arith/Max/max_case.con" as lemma.
75 inline procedural "cic:/Coq/Arith/Max/max_case2.con" as lemma.