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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_isd_nexts.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_isd_nexts.ma
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index 000000000..71c39b335
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+++ b/matita/matita/contribs/lambdadelta/ground/relocation/gr_isd_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/relocation/gr_nexts.ma".
+include "ground/relocation/gr_isd.ma".
+
+(* DIVERGENCE CONDITION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(* Properties with iterated next ********************************************)
+
+(*** isdiv_nexts *)
+lemma gr_isd_nexts (n) (f): 𝛀❪f❫ → 𝛀❪↑*[n]f❫.
+#n @(nat_ind_succ … n) -n /3 width=3 by gr_isd_next/
+qed.
+
+(* Inversion lemmas with iterated next **************************************)
+
+(*** isdiv_inv_nexts *)
+lemma gr_isd_inv_nexts (n) (g): 𝛀❪↑*[n]g❫ → 𝛀❪g❫.
+#n @(nat_ind_succ … n) -n /3 width=3 by gr_isd_inv_next/
+qed-.