--- /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_isi.ma".
+
+(* IDENTITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
+
+(* Constructions with pr_tl *************************************************)
+
+(*** isid_tl *)
+lemma pr_isi_tl (f): 𝐈❪f❫ → 𝐈❪⫰f❫.
+#f cases (pr_map_split_tl f) * #H
+[ /2 width=3 by pr_isi_inv_push/
+| elim (pr_isi_inv_next … H) -H //
+]
+qed.