--- /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/pr_pushs.ma".
+include "ground/relocation/pr_tls.ma".
+
+(* ITERATED TAIL FOR PARTIAL RELOCATION MAPS ********************************)
+
+(* Constructions with pr_pushs **********************************************)
+
+(*** tls_pushs *)
+lemma pr_tls_pushs (n) (f): f = ⫰*[n] ⫯*[n] f.
+#n @(nat_ind_succ … n) -n //
+#n #IH #f <pr_tls_swap <pr_pushs_succ <pr_tl_push //
+qed.