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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_isf_tl.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_isf_tl.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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-.