matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_after.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/substitution/lift_prototerm_eq.ma".
  16 include "delayed_updating/substitution/lift_path_after.ma".
  17
  18 (* LIFT FOR PROTOTERM *******************************************************)
  19
  20 (* Constructions with tr_after **********************************************)
  21
  22 lemma lift_term_after (f) (g) (t):
  23       ↑[g]↑[f]t ⇔ ↑[g∘f]t.
  24 #f #g #t @subset_eq_trans
  25 [
  26 | @subset_inclusion_ext_f1_compose
  27 | @subset_equivalence_ext_f1_exteq /2 width=5/
  28 ]
  29 qed.