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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic_after.ma b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic_after.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/arith/nat_le_pred.ma".
-include "ground/relocation/rtmap_after_uni.ma".
-include "ground/relocation/rtmap_basic.ma".
-
-(* RELOCATION MAP ***********************************************************)
-
-(* Properties with composition **********************************************)
-
-lemma after_basic_rc (m2,m1):
-      m1 ≤ m2 → ∀n2,n1.m2 ≤ n1+m1 → 𝐁❨m2,n2❩ ⊚ 𝐁❨m1,n1❩ ≘ 𝐁❨m1,n1+n2❩.
-#m2 #m1 @(nat_ind_2_succ … m2 m1) -m2 -m1
-[ #m1 #H #n2 #n1 #_
-  <(nle_inv_zero_dx … H) -m1 //
-| #m2 #IH #_ #n2 #n1 <nplus_zero_dx #H
-  elim (nle_inv_succ_sn … H) -H #Hm2 #Hn1
-  >Hn1 -Hn1 <nplus_succ_sn
-  /3 width=7 by after_push/
-| #m2 #m1 #IH #H1 #n2 #n1 <nplus_succ_dx #H2
-  lapply (nle_inv_succ_bi … H1) -H1 #H1
-  lapply (nle_inv_succ_bi … H2) -H2 #H2
-  /3 width=7 by after_refl/
-]
-qed.