matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_eq.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/unwind/unwind2_path_eq.ma".
  18 include "delayed_updating/unwind/unwind2_prototerm.ma".
  19
  20 (* UNWIND FOR PROTOTERM *****************************************************)
  21
  22 (* Constructions with subset_equivalence ************************************)
  23
  24 lemma unwind2_term_eq_repl_sn (f1) (f2) (t):
  25       f1 ≗ f2 → ▼[f1]t ⇔ ▼[f2]t.
  26 /3 width=1 by subset_equivalence_ext_f1_exteq, unwind2_path_eq_repl/
  27 qed.
  28
  29 lemma unwind2_term_eq_repl_dx (f) (t1) (t2):
  30       t1 ⇔ t2 → ▼[f]t1 ⇔ ▼[f]t2.
  31 /2 width=1 by subset_equivalence_ext_f1_bi/
  32 qed.
  33
  34 lemma unwind2_term_after (f1) (f2) (t):
  35       ▼[f2]▼[f1]t ⇔ ▼[f2∘f1]t.
  36 #f1 #f2 #t @subset_eq_trans
  37 [
  38 | @subset_inclusion_ext_f1_compose
  39 | @subset_equivalence_ext_f1_exteq /2 width=5/
  40 ]
  41 qed.