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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_basic.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_basic.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_nat_basic.ma".
+
+(* POSITIVE APPLICATION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(* Properties with gr_basic **********************************************)
+
+(*** at_basic_lt *)
+lemma gr_pat_basic_lt (m) (n) (i):
+      ninj i ≤ m → @❪i, 𝐛❨m,n❩❫ ≘ i.
+#m #n #i >(npsucc_pred i) #Hmi
+/2 width=1 by gr_nat_basic_lt/
+qed.
+
+(*** at_basic_ge *)
+lemma gr_pat_basic_ge (m) (n) (i):
+      m < ninj i → @❪i, 𝐛❨m,n❩❫ ≘ i+n.
+#m #n #i >(npsucc_pred i) #Hmi <nrplus_npsucc_sn
+/3 width=1 by gr_nat_basic_ge, nlt_inv_succ_dx/
+qed.
+
+(* Inversion lemmas with gr_basic ****************************************)
+
+(*** at_basic_inv_lt *)
+lemma gr_pat_basic_inv_lt (m) (n) (i) (j):
+      ninj i ≤ m → @❪i, 𝐛❨m,n❩❫ ≘ j → i = j.
+/3 width=4 by gr_pat_basic_lt, gr_pat_mono/ qed-.
+
+(*** at_basic_inv_ge *)
+lemma gr_pat_basic_inv_ge (m) (n) (i) (j):
+      m < ninj i → @❪i, 𝐛❨m,n❩❫ ≘ j → i+n = j.
+/3 width=4 by gr_pat_basic_ge, gr_pat_mono/ qed-.