helm/software/matita/nlibrary/nat/plus.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/nat.ma".
  16 include "algebra/magmas.ma".
  17
  18 nlet rec plus (n:nat) (m:nat) on n : nat ≝
  19  match n with
  20   [ O ⇒ m
  21   | S n' ⇒ S (plus n' m) ].
  22
  23 ndefinition plus_magma_type: magma_type.
  24  napply mk_magma_type
  25   [ napply NAT
  26   | napply mk_binary_morphism
  27      [ napply plus
  28      | #a; #a'; #b; #b'; #Ha; #Hb; nrewrite < Ha; nrewrite < Hb; napply refl ]##]
  29 nqed.