matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.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 include "delayed_updating/reduction/ifr.ma".
  17 include "delayed_updating/substitution/fsubst_lift.ma".
  18 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
  19
  20 (* DELAYED FOCUSED REDUCTION ************************************************)
  21
  22 lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
  23       t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
  24 #f #p #q #t1 #t2 #H0t1
  25 * #b * #Hb #Ht1 #Ht2
  26 @(ex_intro … (⊗b)) @and3_intro
  27 [ //
  28 | lapply (in_comp_lift_bi f … Ht1) -Ht1 #Ht1
  29 | lapply (eq_lift_bi f … Ht2) -Ht2 #Ht2
  30   @(subset_eq_trans … Ht2) -t2
  31   @(subset_eq_trans … (lift_fsubst …))
  32   [ <structure_append <structure_A_sn <structure_append <structure_L_sn
  33   | //
  34   | /2 width=2 by ex_intro/
  35   | //
  36   ]
  37 ]
  38
  39