matita/matita/contribs/lambdadelta/ground/relocation/pr_pat_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_rplus_succ.ma".
  16 include "ground/relocation/pr_uni.ma".
  17 include "ground/relocation/pr_pat_pat_id.ma".
  18
  19 (* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
  20
  21 (* Constructions with pr_uni ************************************************)
  22
  23 (*** at_uni *)
  24 lemma pr_pat_uni (n) (i):
  25       @❨i,𝐮❨n❩❩ ≘ i+n.
  26 #n @(nat_ind_succ … n) -n
  27 /2 width=5 by pr_pat_next/
  28 qed.
  29
  30 (* Inversions with pr_uni ***************************************************)
  31
  32 (*** at_inv_uni *)
  33 lemma pr_pat_inv_uni (n) (i) (j):
  34       @❨i,𝐮❨n❩❩ ≘ j → j = i+n.
  35 /2 width=4 by pr_pat_mono/ qed-.