matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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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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  14
  15 include "delayed_updating/substitution/lift_path.ma".
  16 include "delayed_updating/syntax/path_closed.ma".
  17 include "ground/relocation/xap.ma".
  18
  19 (* LIFT FOR PATH ************************************************************)
  20
  21 (* Constructions with pcc ***************************************************)
  22
  23 lemma lift_path_closed (f) (q) (n):
  24       q ϵ 𝐂❨n❩ → ↑[f]q ϵ 𝐂❨↑[q]f＠❨n❩❩.
  25 #f #q #n #Hq elim Hq -Hq //
  26 #q #n [ #k ] #_ #IH
  27 /2 width=1 by pcc_d_dx, pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
  28 qed.
  29
  30 lemma lift_path_rmap_closed (f) (p) (q) (n):
  31       q ϵ 𝐂❨n❩ → ↑[↑[p]f]q ϵ 𝐂❨↑[p●q]f＠❨n❩❩.
  32 /2 width=1 by lift_path_closed/
  33 qed.
  34
  35 lemma lift_path_rmap_closed_L (f) (p) (q) (n):
  36       q ϵ 𝐂❨n❩ → ↑[↑[p◖𝗟]f]q ϵ 𝐂❨↑[p●𝗟◗q]f＠§❨n❩❩.
  37 #f #p #q #n #Hq
  38 lapply (lift_path_closed (↑[p◖𝗟]f) … Hq) #Hq0
  39 lapply (pcc_L_sn … Hq) -Hq #Hq1
  40 lapply (lift_path_rmap_closed f p … Hq1) -Hq1
  41 <lift_path_L_sn >lift_rmap_L_dx #Hq1
  42 elim (pcc_inv_L_sn … Hq1 Hq0) -Hq1 #H0 #_
  43 <H0 in Hq0; -H0 //
  44 qed.