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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_length.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_length.ma
new file mode 100644
index 000000000..fe095d1df
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_length.ma
@@ -0,0 +1,33 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2/static/rex_length.ma".
+include "basic_2/rt_transition/rpx.ma".
+
+(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+
+(* Forward lemmas with length for local environments ************************)
+
+lemma rpx_fwd_length: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → |L1| = |L2|.
+/2 width=3 by rex_fwd_length/ qed-.
+
+(* Inversion lemmas with length for local environments **********************)
+
+lemma rpx_inv_zero_length: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
+                           ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+                            | ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 &
+                                               ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 &
+                                               Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
+                            | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+/2 width=1 by rex_inv_zero_length/ qed-.