--- /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_tl.ma".
+include "ground/relocation/pr_isf.ma".
+
+(* FINITE COLENGTH CONDITION FOR PARTIAL RELOCATION MAPS ********************)
+
+(* Constructions with pr_tl *************************************************)
+
+(*** isfin_tl *)
+lemma pr_isf_tl (f): 𝐅❪f❫ → 𝐅❪⫰f❫.
+#f elim (pr_map_split_tl f) * #Hf
+/3 width=3 by pr_isf_inv_push, pr_isf_inv_next/
+qed.
+
+(* Inversions with pr_tl ****************************************************)
+
+(*** isfin_inv_tl *)
+lemma pr_isf_inv_tl (g): 𝐅❪⫰g❫ → 𝐅❪g❫.
+#f elim (pr_map_split_tl f) * #Hf
+/2 width=1 by pr_isf_next, pr_isf_push/
+qed-.