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

   1 (**************************************************************************)
   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                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  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: Minus.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 (*#* Subtraction (difference between two natural numbers) *)
  36
  37 include "Arith/Lt.ma".
  38
  39 include "Arith/Le.ma".
  40
  41 (* UNEXPORTED
  42 Open Local Scope nat_scope.
  43 *)
  44
  45 (* UNEXPORTED
  46 Implicit Types m n p : nat.
  47 *)
  48
  49 (*#* 0 is right neutral *)
  50
  51 inline procedural "cic:/Coq/Arith/Minus/minus_n_O.con" as lemma.
  52
  53 (* UNEXPORTED
  54 Hint Resolve minus_n_O: arith v62.
  55 *)
  56
  57 (*#* Permutation with successor *)
  58
  59 inline procedural "cic:/Coq/Arith/Minus/minus_Sn_m.con" as lemma.
  60
  61 (* UNEXPORTED
  62 Hint Resolve minus_Sn_m: arith v62.
  63 *)
  64
  65 inline procedural "cic:/Coq/Arith/Minus/pred_of_minus.con" as theorem.
  66
  67 (*#* Diagonal *)
  68
  69 inline procedural "cic:/Coq/Arith/Minus/minus_n_n.con" as lemma.
  70
  71 (* UNEXPORTED
  72 Hint Resolve minus_n_n: arith v62.
  73 *)
  74
  75 (*#* Simplification *)
  76
  77 inline procedural "cic:/Coq/Arith/Minus/minus_plus_simpl_l_reverse.con" as lemma.
  78
  79 (* UNEXPORTED
  80 Hint Resolve minus_plus_simpl_l_reverse: arith v62.
  81 *)
  82
  83 (*#* Relation with plus *)
  84
  85 inline procedural "cic:/Coq/Arith/Minus/plus_minus.con" as lemma.
  86
  87 (* UNEXPORTED
  88 Hint Immediate plus_minus: arith v62.
  89 *)
  90
  91 inline procedural "cic:/Coq/Arith/Minus/minus_plus.con" as lemma.
  92
  93 (* UNEXPORTED
  94 Hint Resolve minus_plus: arith v62.
  95 *)
  96
  97 inline procedural "cic:/Coq/Arith/Minus/le_plus_minus.con" as lemma.
  98
  99 (* UNEXPORTED
 100 Hint Resolve le_plus_minus: arith v62.
 101 *)
 102
 103 inline procedural "cic:/Coq/Arith/Minus/le_plus_minus_r.con" as lemma.
 104
 105 (* UNEXPORTED
 106 Hint Resolve le_plus_minus_r: arith v62.
 107 *)
 108
 109 (*#* Relation with order *)
 110
 111 inline procedural "cic:/Coq/Arith/Minus/le_minus.con" as theorem.
 112
 113 inline procedural "cic:/Coq/Arith/Minus/lt_minus.con" as lemma.
 114
 115 (* UNEXPORTED
 116 Hint Resolve lt_minus: arith v62.
 117 *)
 118
 119 inline procedural "cic:/Coq/Arith/Minus/lt_O_minus_lt.con" as lemma.
 120
 121 (* UNEXPORTED
 122 Hint Immediate lt_O_minus_lt: arith v62.
 123 *)
 124
 125 inline procedural "cic:/Coq/Arith/Minus/not_le_minus_0.con" as theorem.
 126