matita/matita/contribs/lambdadelta/ground/relocation/tr_pap_pushs.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/pnat_lt.ma".
  16 include "ground/relocation/tr_pushs.ma".
  17 include "ground/relocation/tr_pap_pn.ma".
  18
  19 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
  20
  21 (* Constructions with tr_pushs **********************************************)
  22
  23 lemma tr_pap_pushs_le (n) (p) (f):
  24       p < ↑n → p = (⫯*[n]f)@❨p❩.
  25 #n @(nat_ind_succ … n) -n
  26 [ #p #f #H0
  27   elim (plt_inv_unit_dx … H0)
  28 | #n #IH *
  29   [ #f #H0 <tr_pushs_succ //
  30   | #p #f <npsucc_succ #H0
  31     lapply (plt_inv_succ_bi … H0) -H0 #H0
  32     lapply (IH … f H0) -IH -H0 #H0
  33     <tr_pushs_succ <tr_pap_push //
  34   ]
  35 ]
  36 qed-.