matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_lift.ma

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   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 "delayed_updating/unwind/preunwind2_rmap_lift.ma".
  17 include "delayed_updating/unwind/preunwind2_rmap_eq.ma".
  18 include "delayed_updating/substitution/lift_path.ma".
  19 include "delayed_updating/syntax/path_structure.ma".
  20
  21 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
  22
  23 (* Constructions with lift_path *********************************************)
  24
  25 lemma lift_unwind2_rmap_after (g) (f) (p):
  26       ↑[⊗p]g∘▶[f]p ≗ ▶[g∘f]p.
  27 #g #f #p elim p -p //
  28 * [ #k ] #p #IH //
  29 [ <unwind2_rmap_d_dx <unwind2_rmap_d_dx
  30   @(stream_eq_canc_sn … (tr_compose_assoc …))
  31   /2 width=1 by tr_compose_eq_repl/
  32 | <unwind2_rmap_L_dx <unwind2_rmap_L_dx <lift_rmap_L_dx
  33   /2 width=1 by tr_push_eq_repl/
  34 ]
  35 qed.
  36
  37 lemma unwind2_lift_rmap_after (g) (f) (p:path):
  38       ▶[g]↑[f]p∘↑[p]f ≗ ▶[g∘f]p.
  39 #g #f #p elim p -p // #l #p #IH
  40 <lift_path_rcons <lift_rmap_rcons <unwind2_rmap_rcons <unwind2_rmap_rcons
  41 @(stream_eq_trans … (preunwind2_lift_rmap_after …))
  42 /2 width=1 by preunwind2_rmap_eq_repl/
  43 qed.