matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_eq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "delayed_updating/unwind/unwind2_rmap.ma".
  16 include "ground/relocation/tr_uni_compose.ma".
  17 include "ground/relocation/tr_compose_eq.ma".
  18 include "ground/relocation/tr_pn_eq.ma".
  19 include "ground/arith/nat_rplus_pplus.ma".
  20
  21 (* UNWIND MAP FOR PATH ******************************************************)
  22
  23 (* Constructions with stream_eq *********************************************)
  24
  25 lemma unwind2_rmap_eq_repl (p):
  26       stream_eq_repl … (λf1,f2. ▶[f1]p ≗ ▶[f2]p).
  27 #p elim p -p //
  28 * [ #n ] #p #IH #f1 #f2 #Hf
  29 [ /3 width=1 by tr_compose_eq_repl/
  30 | /2 width=1 by/
  31 | /3 width=1 by tr_push_eq_repl/
  32 | /2 width=1 by/
  33 | /2 width=1 by/
  34 ]
  35 qed-.
  36
  37 lemma tls_unwind2_rmap_d_sn (f) (p) (m) (n):
  38       ⇂*[m+n]▶[f]p ≗ ⇂*[m]▶[f](𝗱n◗p).
  39 #f #p #m #n
  40 <unwind2_rmap_d_sn >nrplus_inj_dx
  41 /2 width=1 by tr_tls_compose_uni_dx/
  42 qed.