--- /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 "ground/relocation/tr_uni.ma".
+include "ground/relocation/tr_id_pap.ma".
+include "ground/arith/nat_rplus_succ.ma".
+
+(* UNIFORM ELEMENTS FOR TOTAL RELOCATION MAPS *******************************)
+
+(* Coonstructions with tr_pap ***********************************************)
+
+lemma tr_uni_pap_unit (n):
+ ↑n = 𝐮❨n❩@❨𝟏❩.
+// qed.
+
+lemma tr_uni_pap (n) (p):
+ p + n = 𝐮❨n❩@❨p❩.
+#n @(nat_ind_succ … n) -n //
+#n #IH * [| #p ] //
+qed.