--- /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/lift_rmap.ma".
+include "ground/relocation/tr_pap_tls.ma".
+
+(* LIFT FOR RELOCATION MAP **************************************************)
+
+(* Constructions with tr_pap ************************************************)
+
+lemma lift_rmap_pap_d_dx (f) (p) (k) (h):
+ ↑[p]f@⧣❨h+k❩ = ↑[p◖𝗱k]f@⧣❨h❩+↑[p]f@⧣❨k❩.
+// qed.