matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.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/syntax/path_structure.ma".
  16 include "delayed_updating/substitution/lift_eq.ma".
  17
  18 (* LIFT FOR PATH ***********************************************************)
  19
  20 (* Constructions with structure ********************************************)
  21
  22 lemma lift_d_empty_dx (n) (p) (f):
  23       (⊗p)◖𝗱❨(↑[p◖𝗱❨n❩]f)@❨n❩❩ = ↑[f](p◖𝗱❨n❩).
  24 #n #p @(path_ind_lift … p) -p // [ #m #l #p |*: #p ] #IH #f
  25 [ <lift_rmap_d_lcons_sn <lift_path_d_lcons_sn //
  26 | <lift_rmap_L_sn <lift_path_L_sn <IH //
  27 | <lift_rmap_A_sn <lift_path_A_sn <IH //
  28 | <lift_rmap_S_sn <lift_path_S_sn <IH //
  29 ]
  30 qed.
  31
  32 lemma lift_L_dx (p) (f):
  33       (⊗p)◖𝗟 = ↑[f](p◖𝗟).
  34 #p @(path_ind_lift … p) -p // #m #l #p #IH #f
  35 <lift_path_d_lcons_sn //
  36 qed.
  37
  38 lemma lift_A_dx (p) (f):
  39       (⊗p)◖𝗔 = ↑[f](p◖𝗔).
  40 #p @(path_ind_lift … p) -p // #m #l #p #IH #f
  41 <lift_path_d_lcons_sn //
  42 qed.
  43
  44 lemma lift_S_dx (p) (f):
  45       (⊗p)◖𝗦 = ↑[f](p◖𝗦).
  46 #p @(path_ind_lift … p) -p // #m #l #p #IH #f
  47 <lift_path_d_lcons_sn //
  48 qed.
  49
  50 lemma structure_lift (p) (f):
  51       ⊗p = ⊗↑[f]p.
  52 #p @(path_ind_lift … p) -p // #p #IH #f
  53 <lift_path_L_sn //
  54 qed.
  55
  56 lemma lift_structure (p) (f):
  57       ⊗p = ↑[f]⊗p.
  58 #p @(path_ind_lift … p) -p //
  59 qed.