matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_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 include "delayed_updating/unwind/unwind2_path.ma".
  16 include "delayed_updating/unwind/unwind2_rmap_eq.ma".
  17 include "delayed_updating/unwind/unwind_gen_eq.ma".
  18 include "ground/relocation/tr_compose_compose.ma".
  19
  20 (* UNWIND FOR PATH **********************************************************)
  21
  22 (* Constructions with stream_eq *********************************************)
  23
  24 lemma unwind2_path_eq_repl (p):
  25       stream_eq_repl … (λf1,f2. ▼[f1]p = ▼[f2]p).
  26 /3 width=1 by unwind2_rmap_eq_repl, unwind_gen_eq_repl/
  27 qed-.
  28
  29 (* Properties with tr_compose ***********************************************)
  30
  31 lemma unwind2_path_after (p) (f1) (f2):
  32       ▼[f2]▼[f1]p = ▼[f2∘f1]p.
  33 #p @(path_ind_unwind … p) -p // [ #n #l #p | #p ] #IH #f1 #f2
  34 [ <unwind2_path_d_lcons <unwind2_path_d_lcons
  35   >(unwind2_path_eq_repl … (tr_compose_assoc …)) //
  36 | <(unwind2_path_L_sn … f1) <unwind2_path_L_sn <unwind2_path_L_sn
  37   >tr_compose_push_bi //
  38 ]
  39 qed.