helm/software/matita/nlibrary/nat/compare.ma

   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 include "nat/order.ma".
  16 include "datatypes/bool.ma".
  17
  18 naxiom decompose1: ¬(lt O O).
  19 naxiom decompose2: ∀n. ¬(lt (S n) O).
  20
  21 ndefinition ltb: nat → nat → bool.
  22  #n; nelim n
  23   [ #m; ncases m
  24     [ napply false
  25     | #m'; napply true ]
  26 ##| #n'; #Hn'; #m; ncases m
  27     [ napply false
  28     | #m'; ncases (Hn' m')
  29        [ napply true
  30        | napply false]##]
  31 nqed.