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:                                           *)
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   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 "delayed_updating/syntax/path_structure.ma".
  17 include "delayed_updating/syntax/path_proper.ma".
  18
  19 (* LIFT FOR PATH ***********************************************************)
  20
  21 (* Basic constructions with structure **************************************)
  22
  23 lemma structure_lift (p) (f):
  24       ⊗p = ⊗↑[f]p.
  25 #p @(path_ind_lift … p) -p // #p #IH #f
  26 <lift_path_L_sn //
  27 qed.
  28
  29 lemma lift_structure (p) (f):
  30       ⊗p = ↑[f]⊗p.
  31 #p @(path_ind_lift … p) -p //
  32 qed.
  33
  34 (* Properties with proper condition for path ********************************)
  35
  36 lemma lift_append_proper_dx (p2) (p1) (f): Ꝕp2 →
  37       (⊗p1)●(↑[↑[p1]f]p2) = ↑[f](p1●p2).
  38 #p2 #p1 @(path_ind_lift … p1) -p1 //
  39 [ #n | #n #l #p1 |*: #p1 ] #IH #f #Hp2
  40 [ elim (ppc_inv_lcons … Hp2) -Hp2 #l #q #H destruct //
  41 | <lift_path_d_lcons_sn <IH //
  42 | <lift_path_L_sn <IH //
  43 | <lift_path_A_sn <IH //
  44 | <lift_path_S_sn <IH //
  45 ]
  46 qed-.
  47
  48 (* Advanced constructions with structure ************************************)
  49
  50 lemma lift_d_empty_dx (n) (p) (f):
  51       (⊗p)◖𝗱((↑[p]f)@❨n❩) = ↑[f](p◖𝗱n).
  52 /3 width=3 by ppc_lcons, lift_append_proper_dx/
  53 qed.
  54
  55 lemma lift_L_dx (p) (f):
  56       (⊗p)◖𝗟 = ↑[f](p◖𝗟).
  57 /3 width=3 by ppc_lcons, lift_append_proper_dx/
  58 qed.
  59
  60 lemma lift_A_dx (p) (f):
  61       (⊗p)◖𝗔 = ↑[f](p◖𝗔).
  62 /3 width=3 by ppc_lcons, lift_append_proper_dx/
  63 qed.
  64
  65 lemma lift_S_dx (p) (f):
  66       (⊗p)◖𝗦 = ↑[f](p◖𝗦).
  67 /3 width=3 by ppc_lcons, lift_append_proper_dx/
  68 qed.