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

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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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 (o) (f) (q) (n):
  24       q ϵ 𝐂❨o,n❩ → 🠡[f]q ϵ 𝐂❨o,🠢[f]q＠❨n❩❩.
  25 #o #f #q #n #H0 elim H0 -q -n //
  26 #q #n [ #k #Ho ] #_ #IH
  27 /2 width=1 by pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
  28 /4 width=1 by pcc_d_dx, tr_xap_pos/
  29 qed.
  30
  31 lemma lift_path_rmap_closed (o) (f) (p) (q) (n):
  32       q ϵ 𝐂❨o,n❩ → 🠡[🠢[f]p]q ϵ 𝐂❨o,🠢[f](p●q)＠❨n❩❩.
  33 /2 width=1 by lift_path_closed/
  34 qed.
  35
  36 lemma lift_path_rmap_closed_L (o) (f) (p) (q) (n):
  37       q ϵ 𝐂❨o,n❩ → 🠡[🠢[f](p◖𝗟)]q ϵ 𝐂❨o,🠢[f](p●𝗟◗q)＠§❨n❩❩.
  38 #o #f #p #q #n #Hq
  39 lapply (lift_path_closed … (🠢[f](p◖𝗟)) … Hq) #Hq0
  40 lapply (pcc_L_sn … Hq) -Hq #Hq1
  41 lapply (lift_path_rmap_closed … f p … Hq1) -Hq1
  42 <lift_path_L_sn >lift_rmap_L_dx #Hq1
  43 elim (pcc_inv_L_sn … Hq1 Hq0) -Hq1 #H0 #_
  44 <H0 in Hq0; -H0 //
  45 qed.