matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_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       *)
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  13 (**************************************************************************)
  14
  15 include "delayed_updating/reduction/ifr.ma".
  16
  17 include "delayed_updating/substitution/fsubst_lift.ma".
  18 include "delayed_updating/substitution/fsubst_eq.ma".
  19 include "delayed_updating/substitution/lift_prototerm_after.ma".
  20 include "delayed_updating/substitution/lift_path_head.ma".
  21 include "delayed_updating/substitution/lift_rmap_head.ma".
  22
  23 include "ground/relocation/tr_uni_compose.ma".
  24 include "ground/relocation/tr_compose_eq.ma".
  25
  26 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
  27
  28 (* Constructions with lift **************************************************)
  29
  30 theorem ifr_lift_bi (f) (t1) (t2) (r):
  31         t1 ➡𝐢𝐟[r] t2 → ↑[f]t1 ➡𝐢𝐟[↑[f]r] ↑[f]t2.
  32 #f #t1 #t2 #r
  33 * #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
  34 @(ex4_3_intro … (↑[f]p) (↑[↑[p◖𝗔◖𝗟]f]q) ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨k❩))
  35 [ -H1k -Ht1 -Ht2 //
  36 | -Ht1 -Ht2
  37   <lift_rmap_L_dx >lift_path_L_sn
  38   <(lift_path_head_closed … H1k) in ⊢ (??%?); -H1k //
  39 | lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1k
  40   <lift_path_d_dx #Ht1 //
  41 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
  42   @(subset_eq_trans … Ht2) -t2
  43   @(subset_eq_trans … (lift_term_fsubst …))
  44   @fsubst_eq_repl [ // | <lift_path_append // ]
  45   @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
  46   [ @lift_term_grafted_S | skip ]
  47   @(subset_eq_trans … (lift_term_after …))
  48   @(subset_eq_canc_dx … (lift_term_after …))
  49   @lift_term_eq_repl_sn
  50 (* Note: crux of the proof begins *)
  51   @(stream_eq_trans … (tr_compose_uni_dx …))
  52   @tr_compose_eq_repl //
  53   >list_append_rcons_sn in H1k; #H1k >lift_rmap_A_dx
  54   /2 width=1 by tls_lift_rmap_closed/
  55 (* Note: crux of the proof ends *)
  56 ]
  57 qed.