helm/software/matita/contribs/procedural/Coq/Num/Nat/Axioms.mma

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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "Coq.ma".
  18
  19 (*i $Id: i*)
  20
  21 (*s Axioms for the basic numerical operations *)
  22
  23 include "Num/Params.ma".
  24
  25 include "Num/EqAxioms.ma".
  26
  27 include "Num/NSyntax.ma".
  28
  29 (*s Lemmas for [add] *)
  30
  31 inline procedural "cic:/Coq/Num/Nat/Axioms/add_Sx_y.con" as lemma.
  32
  33 (* UNEXPORTED
  34 Hints Resolve add_Sx_y : nat.
  35 *)
  36
  37 (*s Lemmas for [add] *)
  38
  39 inline procedural "cic:/Coq/Num/Nat/Axioms/add_0_x.con" as lemma.
  40
  41 (* UNEXPORTED
  42 Hints Resolve add_0_x : nat.
  43 *)
  44
  45 inline procedural "cic:/Coq/Num/Nat/Axioms/add_sym.con" as lemma.
  46
  47 (* UNEXPORTED
  48 Hints Resolve add_sym : nat.
  49 *)
  50
  51 inline procedural "cic:/Coq/Num/Nat/Axioms/add_eq_compat.con" as lemma.
  52
  53 (* UNEXPORTED
  54 Hints Resolve add_eq_compat : nat.
  55 *)
  56
  57 inline procedural "cic:/Coq/Num/Nat/Axioms/add_assoc_l.con" as lemma.
  58
  59 (*s Lemmas for [one] *)
  60
  61 inline procedural "cic:/Coq/Num/Nat/Axioms/S_0_1.con" as lemma.
  62
  63 (*s Lemmas for [<],
  64     properties of [>], [<=] and [>=] will be derived from [<] *)
  65
  66 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_trans.con" as lemma.
  67
  68 (* UNEXPORTED
  69 Hints Resolve lt_trans : nat.
  70 *)
  71
  72 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_x_Sx.con" as lemma.
  73
  74 (* UNEXPORTED
  75 Hints Resolve lt_x_Sx : nat.
  76 *)
  77
  78 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_S_compat.con" as lemma.
  79
  80 (* UNEXPORTED
  81 Hints Resolve lt_S_compat : nat.
  82 *)
  83
  84 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_eq_compat.con" as lemma.
  85
  86 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_add_compat_l.con" as lemma.
  87
  88 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_Sx_Sy_lt.con" as lemma.
  89
  90 (* UNEXPORTED
  91 Hints Immediate lt_Sx_Sy_lt : nat.
  92 *)
  93
  94 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_anti_refl.con" as lemma.
  95