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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_path_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_path_after.ma
new file mode 100644
index 000000000..955f4b1c8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_path_after.ma
@@ -0,0 +1,28 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/unwind_k/unwind2_path_eq.ma".
+include "delayed_updating/unwind_k/unwind2_rmap_after.ma".
+
+(* TAILED UNWIND FOR PATH ***************************************************)
+
+(* Properties with tr_after *************************************************)
+
+lemma unwind2_path_after (g) (f) (p):
+      ▼[g]▼[f]p = ▼[g∘f]p.
+#g #f * // * [ #k ] #p //
+<unwind2_path_d_dx <unwind2_path_d_dx
+@eq_f2 // @eq_f >tr_compose_pap
+/2 width=3 by tr_pap_eq_repl/
+qed.