helm/software/matita/contribs/procedural/Coq/Arith/Min.mma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "Coq.ma".
  18
  19 (*#***********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  22
  23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  24
  25 (*   \VV/  **************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the       *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1        *)
  30
  31 (*#***********************************************************************)
  32
  33 (*i $Id: Min.v,v 1.10.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 include "Arith/Arith.ma".
  36
  37 (* UNEXPORTED
  38 Open Local Scope nat_scope.
  39 *)
  40
  41 (* UNEXPORTED
  42 Implicit Types m n : nat.
  43 *)
  44
  45 (*#* minimum of two natural numbers *)
  46
  47 inline procedural "cic:/Coq/Arith/Min/min.con" as definition.
  48
  49 (*#* Simplifications of [min] *)
  50
  51 inline procedural "cic:/Coq/Arith/Min/min_SS.con" as lemma.
  52
  53 inline procedural "cic:/Coq/Arith/Min/min_comm.con" as lemma.
  54
  55 (*#* [min] and [le] *)
  56
  57 inline procedural "cic:/Coq/Arith/Min/min_l.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Arith/Min/min_r.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Arith/Min/le_min_l.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Arith/Min/le_min_r.con" as lemma.
  64
  65 (* UNEXPORTED
  66 Hint Resolve min_l min_r le_min_l le_min_r: arith v62.
  67 *)
  68
  69 (*#* [min n m] is equal to [n] or [m] *)
  70
  71 inline procedural "cic:/Coq/Arith/Min/min_dec.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Arith/Min/min_case.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Arith/Min/min_case2.con" as lemma.
  76