--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+include "delayed_updating/substitution/prelift_rmap_after.ma".
+include "delayed_updating/substitution/lift_path.ma".
+
+(* LIFT FOR RELOCATION MAP **************************************************)
+
+(* Constructions with tr_after **********************************************)
+
+lemma lift_rmap_after (g) (f) (p:path):
+ ↑[↑[f]p]g∘↑[p]f = ↑[p](g∘f).
+#g #f #p elim p -p //
+#l #p #IH
+<lift_rmap_rcons //
+qed.