matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.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/reduction/dfr.ma".
  16
  17 include "delayed_updating/substitution/fsubst_lift.ma".
  18 include "delayed_updating/substitution/fsubst_eq.ma".
  19 include "delayed_updating/substitution/lift_constructors.ma".
  20 include "delayed_updating/substitution/lift_path_closed.ma".
  21 include "delayed_updating/substitution/lift_rmap_closed.ma".
  22
  23 (* DELAYED FOCUSED REDUCTION ************************************************)
  24
  25 (* Constructions with lift **************************************************)
  26
  27 theorem dfr_lift_bi (f) (t1) (t2) (r):
  28         t1 ➡𝐝𝐟[r] t2 → 🠡[f]t1 ➡𝐝𝐟[🠡[f]r] 🠡[f]t2.
  29 #f #t1 #t2 #r
  30 * #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
  31 @(ex4_3_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔◖𝗟)]q) (🠢[f](p●𝗔◗𝗟◗q)＠§❨n❩))
  32 [ -Hn -Ht1 -Ht2 //
  33 | -Ht1 -Ht2
  34   /2 width=1 by lift_path_rmap_closed_L/
  35 | lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -Hn
  36   <lift_path_d_dx #Ht1 //
  37 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
  38   @(subset_eq_trans … Ht2) -t2
  39   @(subset_eq_trans … (lift_term_fsubst …))
  40   @fsubst_eq_repl [ // | // ]
  41   @(subset_eq_trans … (lift_term_iref_nap …))
  42   @iref_eq_repl
  43   @(subset_eq_canc_sn … (lift_term_grafted_S …))
  44   @lift_term_eq_repl_sn
  45 (* Note: crux of the proof begins *)
  46   /2 width=2 by tls_succ_lift_rmap_append_closed_Lq_dx/
  47 (* Note: crux of the proof ends *)
  48 ]
  49 qed.