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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nexts.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_nexts.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/notation/functions/uparrowstar_2.ma".
+include "ground/arith/nat_succ_iter.ma".
+include "ground/relocation/gr_map.ma".
+
+(* ITERATED NEXT FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(*** nexts *)
+definition gr_nexts (f:gr_map) (n:nat) ≝
+           (gr_next^n) f.
+
+interpretation
+  "iterated next (generic relocation maps)"
+  'UpArrowStar n f = (gr_nexts f n).
+
+(* Basic properties *********************************************************)
+
+(*** nexts_O *)
+lemma gr_nexts_zero:
+      ∀f. f = ↑*[𝟎] f.
+// qed.
+
+(*** nexts_swap *)
+lemma gr_nexts_next (n):
+      ∀f. ↑↑*[n] f = ↑*[n] ↑f.
+#f #n @(niter_appl … gr_next)
+qed.
+
+(*** nexts_S *)
+lemma gr_nexts_succ (n):
+      ∀f. ↑↑*[n] f = ↑*[↑n] f.
+#f #n @(niter_succ … gr_next)
+qed.
+
+(*** nexts_xn *)
+lemma gr_nexts_swap (n):
+      ∀f. ↑*[n] ↑f = ↑*[↑n] f.
+// qed.