--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.tcs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "ground/arith/nat_rplus_succ.ma".
+include "ground/relocation/rtmap_uni.ma".
+include "ground/relocation/rtmap_at.ma".
+
+(* RELOCATION MAP ***********************************************************)
+
+(* Properties with uniform relocations **************************************)
+
+lemma at_uni: ∀n,i. @❪i,𝐔❨n❩❫ ≘ i+n.
+#n @(nat_ind_succ … n) -n /2 width=5 by at_next/
+qed.
+
+(* Inversion lemmas with uniform relocations ********************************)
+
+lemma at_inv_uni: ∀n,i,j. @❪i,𝐔❨n❩❫ ≘ j → j = i+n.
+/2 width=4 by at_mono/ qed-.