propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / rtmap_nat_uni.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_nat_uni.ma b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_nat_uni.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.tcs.unibo.it                            *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground/arith/nat_plus.ma".
+include "ground/relocation/rtmap_uni.ma".
+include "ground/relocation/rtmap_nat.ma".
+
+(* NON-NEGATIVE APPLICATION FOR RELOCATION MAPS *****************************)
+
+(* Properties with uniform relocations **************************************)
+
+lemma rm_nat_uni (n) (l): @↑❪l,𝐔❨n❩❫ ≘ l+n.
+#n @(nat_ind_succ … n) -n /2 width=5 by rm_nat_next/
+qed.
+
+(* Inversion lemmas with uniform relocations ********************************)
+
+lemma rm_nat_inv_uni (n) (l) (k): @↑❪l,𝐔❨n❩❫ ≘ k → k = l+n.
+/2 width=4 by rm_nat_mono/ qed-.