--- /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/gr_pushs.ma".
+include "ground/relocation/gr_isf.ma".
+
+(* FINITE COLENGTH CONDITION FOR GENERIC RELOCATION MAPS *)
+
+(* Properties with iterated push ********************************************)
+
+(*** isfin_pushs *)
+lemma gr_isf_pushs (n) (f): 𝐅❪f❫ → 𝐅❪⫯*[n]f❫.
+#n @(nat_ind_succ … n) -n /3 width=3 by gr_isf_push/
+qed.
+
+(* Inversion lemmas with iterated push **************************************)
+
+(*** isfin_inv_pushs *)
+lemma gr_isf_inv_pushs (n) (g): 𝐅❪⫯*[n]g❫ → 𝐅❪g❫.
+#n @(nat_ind_succ … n) -n /3 width=3 by gr_isf_inv_push/
+qed-.