matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_crux.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                             *)
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  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_rmap_closed.ma".
  16 include "delayed_updating/unwind/unwind2_rmap_guard.ma".
  17
  18 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
  19
  20 (* Crucial constructions with tr_uni ****************************************)
  21
  22 (* Note: crux of the commutation between unwind and balanced focused reduction *)
  23 lemma unwind2_rmap_uni_crux (f) (p) (b) (q) (m) (n):
  24       p ϵ 𝐆 → b ϵ 𝐂❨Ⓕ,m❩ → q ϵ 𝐂❨Ⓕ,n❩ →
  25       (𝐮❨↑(♭b+♭q)❩ ∘ ▶[⫯f]p ≗ ▶[⫯f](p●𝗔◗b●𝗟◗q) ∘ 𝐮❨↑(m+n)❩).
  26 #f #p #b #q #m #n #Hp #Hm #Hn
  27 <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
  28 >list_append_rcons_sn >(list_append_rcons_sn … b)
  29 @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
  30 @(stream_eq_trans ????? (tr_compose_eq_repl …))
  31 [| @tls_succ_plus_unwind2_rmap_append_closed_Lq_dx // | skip
  32 |  <nap_plus_unwind2_rmap_append_closed_Lq_dx // | skip
  33 ] -Hn
  34 @tr_eq_inv_nap_zero_tl_bi
  35 [ <tr_compose_nap <tr_compose_nap <tr_uni_nap <tr_uni_nap
  36   <nap_zero_unwind2_rmap_push_guard // <nplus_zero_sn
  37   >nsucc_unfold >nplus_succ_dx >nplus_succ_dx <nplus_assoc
  38   >tr_nap_plus_dx <unwind2_rmap_append
  39   <nap_plus_unwind2_rmap_closed [|*: /2 width=2 by pcc_A_sn/ ]
  40   <nap_zero_unwind2_rmap_push_guard //
  41 | @(stream_eq_canc_sn … (tr_tl_compose_uni_sn …))
  42   @(stream_eq_trans ????? (tr_tl_compose_uni_sn …))
  43   >stream_tls_succ <unwind2_rmap_append <unwind2_rmap_push_guard
  44   /2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
  45 ]
  46 qed-.