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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat_nat.ma b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat_nat.ma
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index 000000000..1dd3cd9a6
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+++ b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat_nat.ma
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/fr2_nat.ma".
+
+(* NON-NEGATIVE APPLICATION FOR FINITE RELOCATION MAPS WITH PAIRS *******************************************)
+
+(* Main properties **********************************************************)
+
+(*** at_mono *)
+theorem fr2_nat_mono (f) (l):
+        ∀l1. @❪l, f❫ ≘ l1 → ∀l2. @❪l, f❫ ≘ l2 → l1 = l2.
+#f #l #l1 #H elim H -f -l -l1
+[ #l #x #H <(fr2_nat_inv_nil … H) -x //
+| #f #d #h #l #l1 #Hld #_ #IH #x #H
+  lapply (fr2_nat_inv_cons_lt … H Hld) -H -Hld /2 width=1 by/
+| #f #d #h #l #l1 #Hdl #_ #IH #x #H
+  lapply (fr2_nat_inv_cons_ge … H Hdl) -H -Hdl /2 width=1 by/
+]
+qed-.