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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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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: Min.v,v 1.10.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
35 include "Arith/Arith.ma".
38 Open Local Scope nat_scope.
42 Implicit Types m n : nat.
45 (*#* minimum of two natural numbers *)
47 inline procedural "cic:/Coq/Arith/Min/min.con" as definition.
49 (*#* Simplifications of [min] *)
51 inline procedural "cic:/Coq/Arith/Min/min_SS.con" as lemma.
53 inline procedural "cic:/Coq/Arith/Min/min_comm.con" as lemma.
55 (*#* [min] and [le] *)
57 inline procedural "cic:/Coq/Arith/Min/min_l.con" as lemma.
59 inline procedural "cic:/Coq/Arith/Min/min_r.con" as lemma.
61 inline procedural "cic:/Coq/Arith/Min/le_min_l.con" as lemma.
63 inline procedural "cic:/Coq/Arith/Min/le_min_r.con" as lemma.
66 Hint Resolve min_l min_r le_min_l le_min_r: arith v62.
69 (*#* [min n m] is equal to [n] or [m] *)
71 inline procedural "cic:/Coq/Arith/Min/min_dec.con" as lemma.
73 inline procedural "cic:/Coq/Arith/Min/min_case.con" as lemma.
75 inline procedural "cic:/Coq/Arith/Min/min_case2.con" as lemma.