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(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
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include "delayed_updating/substitution/lift_eq.ma".
include "ground/relocation/tr_compose_pap.ma".
include "ground/relocation/tr_compose_pn.ma".

(* LIFT FOR PATH ************************************************************)

(* Constructions with tr_after **********************************************)

lemma lift_path_after (p) (f1) (f2):
      ↑[f2]↑[f1]p = ↑[f2∘f1]p.
#p elim p -p [| * ] // #p #IH #f1 #f2
<lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
>tr_compose_push_bi //
qed.