matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_after.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 "delayed_updating/substitution/lift_eq.ma".
  16 include "ground/relocation/tr_compose_pap.ma".
  17 include "ground/relocation/tr_compose_pn.ma".
  18 include "ground/relocation/tr_compose_tls.ma".
  19
  20 (* LIFT FOR PATH ***********************************************************)
  21
  22 (* Constructions with tr_after *********************************************)
  23
  24 lemma lift_path_after (p) (f1) (f2):
  25       ↑[f2]↑[f1]p = ↑[f2∘f1]p.
  26 #p elim p -p [| * ] // [ #n ] #p #IH #f1 #f2
  27 [ <lift_path_d_sn <lift_path_d_sn <lift_path_d_sn //
  28 | <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
  29   >tr_compose_push_bi //
  30 ]
  31 qed.