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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_eq.ma
new file mode 100644
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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 "delayed_updating/substitution/lift_rmap.ma".
+include "ground/relocation/tr_pn_eq.ma".
+include "ground/lib/stream_tls_plus.ma".
+include "ground/lib/stream_tls_eq.ma".
+include "ground/arith/nat_plus_rplus.ma".
+include "ground/arith/nat_rplus_pplus.ma".
+
+(* LIFT FOR RELOCATION MAP **************************************************)
+
+(* Constructions with lift_eq ***********************************************)
+
+lemma lift_rmap_eq_repl (p):
+      stream_eq_repl … (λf1,f2. ↑[p]f1 ≗ ↑[p]f2).
+#p elim p -p //
+* [ #k ] #p #IH #f1 #f2 #Hf
+[ /3 width=1 by stream_tls_eq_repl/
+| /2 width=1 by/
+| /3 width=1 by tr_push_eq_repl/
+| /2 width=1 by/
+| /2 width=1 by/
+]
+qed.
+
+lemma tls_lift_rmap_d_dx (f) (p) (n) (k):
+      ⇂*[n+k]↑[p]f ≗ ⇂*[n]↑[p◖𝗱k]f.
+#f #p #n #k
+<lift_rmap_d_dx >nrplus_inj_dx >nrplus_inj_sn //
+qed.