matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure_depth.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.ma".
  16 include "delayed_updating/syntax/path_structure.ma".
  17 include "delayed_updating/syntax/path_depth.ma".
  18 include "ground/relocation/tr_pushs.ma".
  19 include "ground/arith/nat_pred_succ.ma".
  20
  21 (* LIFT FOR PATH ***********************************************************)
  22
  23 (* Basic constructions with structure and depth ****************************)
  24
  25 lemma lift_rmap_structure (p) (f):
  26       (⫯*[↓❘p❘]f) = ↑[⊗p]f.
  27 #p elim p -p //
  28 * [ #n ] #p #IH #f //
  29 [ <lift_rmap_L_sn <IH -IH >tr_pushs_swap //
  30 | <lift_rmap_A_sn //
  31 | <lift_rmap_S_sn //
  32 ]
  33 qed.