matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_uni.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 "ground/arith/nat_plus_rplus.ma".
  16 include "ground/relocation/gr_pat_uni.ma".
  17 include "ground/relocation/gr_nat_nat.ma".
  18
  19 (* NON-NEGATIVE APPLICATION FOR GENERIC RELOCATION MAPS *********************)
  20
  21 (* Constructions with gr_uni ************************************************)
  22
  23 lemma gr_nat_uni (n) (l):
  24       @↑❪l,𝐮❨n❩❫ ≘ l+n.
  25 /2 width=1 by gr_nat_pred_bi/
  26 qed.
  27
  28 (* Inversions with gr_uni ***************************************************)
  29
  30 lemma gr_nat_inv_uni (n) (l) (k):
  31       @↑❪l,𝐮❨n❩❫ ≘ k → k = l+n.
  32 /2 width=4 by gr_nat_mono/ qed-.