(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_gen_eq.ma".
-include "ground/relocation/tr_compose_pap.ma".
-include "ground/relocation/tr_compose_pn.ma".
-include "ground/relocation/tr_compose_tls.ma".
+include "delayed_updating/substitution/lift_rmap_after.ma".
+include "delayed_updating/substitution/prelift_label_after.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 [| * ] // [ #n ] #p #IH #f1 #f2
-[ <lift_path_d_sn <lift_path_d_sn <lift_path_d_sn //
-| <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
- >tr_compose_push_bi //
-]
+lemma lift_path_after (g) (f) (p):
+ ↑[g]↑[f]p = ↑[g∘f]p.
+#g #f #p elim p -p //
+#l #p #IH
+<lift_path_rcons <lift_path_rcons <IH -IH //
qed.