--- /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_isi.ma".
+
+(* IDENTITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
+
+(* Constructions with pr_pushs **********************************************)
+
+(*** isid_pushs *)
+lemma pr_isi_pushs (n) (f): 𝐈❪f❫ → 𝐈❪⫯*[n]f❫.
+#n @(nat_ind_succ … n) -n /3 width=3 by pr_isi_push/
+qed.
+
+(* Inversions with pr_pushs *************************************************)
+
+(*** isid_inv_pushs *)
+lemma pr_isi_inv_pushs (n) (g): 𝐈❪⫯*[n]g❫ → 𝐈❪g❫.
+#n @(nat_ind_succ … n) -n /3 width=3 by pr_isi_inv_push/
+qed-.