matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_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 (**) (* reverse include *)
  16 include "ground/lib/subset_ext_equivalence.ma".
  17 include "delayed_updating/substitution/lift_prototerm.ma".
  18 include "delayed_updating/unwind/unwind2_path_lift.ma".
  19 include "delayed_updating/unwind/unwind2_prototerm.ma".
  20
  21 (* TAILED UNWIND FOR PROTOTERM **********************************************)
  22
  23 (* Constructions with lift_prototerm ****************************************)
  24
  25 lemma lift_unwind2_term_after (f1) (f2) (t):
  26       🠡[f2]▼[f1]t ⇔ ▼[f2∘f1]t.
  27 #f1 #f2 #t @subset_eq_trans
  28 [| @subset_inclusion_ext_f1_compose ]
  29 @subset_equivalence_ext_f1_exteq #p
  30 @lift_unwind2_path_after
  31 qed.
  32
  33 lemma unwind2_lift_term_after (f1) (f2) (t):
  34       ▼[f2]🠡[f1]t ⇔ ▼[f2∘f1]t.
  35 #f1 #f2 #t @subset_eq_trans
  36 [| @subset_inclusion_ext_f1_compose ]
  37 @subset_equivalence_ext_f1_exteq #p
  38 @unwind2_lift_path_after
  39 qed.