matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.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_path.ma".
  16 include "delayed_updating/syntax/path_proper.ma".
  17
  18 (* LIFT FOR PATH ************************************************************)
  19
  20 (* Constructions with proper condition for path *****************************)
  21
  22 lemma lift_path_proper (f) (p):
  23       p ϵ 𝐏 → 🠡[f]p ϵ 𝐏.
  24 #f *
  25 [ #H0 elim (ppc_inv_empty … H0)
  26 | * [ #k ] #p #_
  27   [ <lift_path_d_dx
  28   | <lift_path_m_dx
  29   | <lift_path_L_dx
  30   | <lift_path_A_dx
  31   | <lift_path_S_dx
  32   ]
  33   /2 width=3 by ppc_rcons/
  34 ]
  35 qed.
  36
  37 (* Inversions with proper condition for path ********************************)
  38
  39 lemma lift_path_inv_proper (f) (p):
  40       🠡[f]p ϵ 𝐏 → p ϵ 𝐏.
  41 #f * //
  42 #H0 elim (ppc_inv_empty … H0)
  43 qed-.