helm/software/matita/contribs/RELATIONAL-ARITHMETICS/add_defs.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 set "baseuri" "cic:/matita/RELATIONAL-ARITHMETICS/add_defs".
  16
  17 include "nat_defs.ma".
  18
  19 inductive add (p:nat): nat \to nat \to Prop \def
  20    | add_O_2: add p O p
  21    | add_S_2: \forall q, r. add p q r \to add p (S q) (S r).