--- /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_tls.ma".
+include "ground/relocation/pr_isf_tl.ma".
+
+(* FINITE COLENGTH CONDITION FOR PARTIAL RELOCATION MAPS ********************)
+
+(* Constructions with pr_tls ************************************************)
+
+lemma pr_isf_tls (n) (f): 𝐅❪f❫ → 𝐅❪⫰*[n]f❫.
+#n @(nat_ind_succ … n) -n /3 width=1 by pr_isf_tl/
+qed.
+
+(* Inversions with pr_tls ***************************************************)
+
+(*** isfin_inv_tls *)
+lemma pr_isf_inv_tls (n) (g): 𝐅❪⫰*[n]g❫ → 𝐅❪g❫.
+#n @(nat_ind_succ … n) -n /3 width=1 by pr_isf_inv_tl/
+qed-.