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diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_basic_after.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_basic_after.ma
new file mode 100644
index 000000000..788d8c24f
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_basic_after.ma
@@ -0,0 +1,39 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2/relocation/rtmap_after.ma".
+include "ground_2/relocation/rtmap_basic.ma".
+
+(* RELOCATION MAP ***********************************************************)
+
+(* Properties with composition **********************************************)
+
+lemma after_basic_rc (m2,m1,n2,n1):
+                     m1 ≤ m2 → m2 ≤ m1+n1 → 𝐁❴m2,n2❵ ⊚ 𝐁❴m1,n1❵ ≘ 𝐁❴m1,n2+n1❵.
+#m2 elim m2 -m2
+[ #m1 #n2 #n1 #Hm21 #_
+  <(le_n_O_to_eq … Hm21) -m1 //
+| #m2 #IH *
+  [ #n2 #n1 #_ < plus_O_n #H
+    elim (le_inv_S1 … H) -H #x #Hx #H destruct
+    <plus_n_Sm
+    @after_push [4:|*: // ]
+    @(IH 0 … Hx) -IH -n2 -x //
+  | #m1 #n2 #n1 #H1 #H2
+    lapply (le_S_S_to_le … H1) -H1 #H1
+    lapply (le_S_S_to_le … H2) -H2 #H2
+    /3 width=7 by after_refl/
+  ]
+]
+qed.