matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind_gen_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/unwind_gen.ma".
  16 include "ground/relocation/tr_pap_eq.ma".
  17
  18 (* GENERIC UNWIND FOR PATH **************************************************)
  19
  20 (* Constructions with stream_eq *********************************************)
  21
  22 lemma unwind_gen_eq_repl (p) (f1) (f2):
  23       (∀n. f1 n ≗ f2 n) → ◆[f1]p = ◆[f2]p.
  24 #p @(path_ind_unwind … p) -p // [ #n | #n #l #p |*: #p ] #IH #f1 #f2 #Hf
  25 [ <unwind_gen_d_empty <unwind_gen_d_empty
  26   <(tr_pap_eq_repl … (Hf n)) -f2 -IH //
  27 | <unwind_gen_d_lcons <unwind_gen_d_lcons
  28   <(IH … Hf) -f2 -IH //
  29 | <unwind_gen_m_sn <unwind_gen_m_sn
  30   <(IH … Hf) -f2 -IH //
  31 | <unwind_gen_L_sn <unwind_gen_L_sn
  32   <(IH … Hf) -f2 -IH //
  33 | <unwind_gen_A_sn <unwind_gen_A_sn
  34   <(IH … Hf) -f2 -IH //
  35 | <unwind_gen_S_sn <unwind_gen_S_sn
  36   <(IH … Hf) -f2 -IH //
  37 ]
  38 qed-.