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diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.ma
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index 000000000..99ad5a092
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+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.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_2/steps/rtc_shift.ma".
+include "ground_2/steps/rtc_ist.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+(* Properties with test for t-transition counter ****************************)
+
+lemma ist_zero_shift: ∀c. 𝐓⦃0,c⦄ → 𝐓⦃0,↕*c⦄.
+#c #H destruct //
+qed.
+
+(* Inversion properties with test for t-transition counter ******************)
+
+lemma ist_inv_shift: ∀n,c. 𝐓⦃n,↕*c⦄ → ∧∧ 𝐓⦃0,c⦄ & 0 = n.
+#n #c #H
+elim (shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #H1 #_ #H2 #H3 #H4 destruct
+elim (max_inv_O3 … H1) -H1 #H11 #H12 destruct
+elim (max_inv_O3 … H2) -H2 #H21 #H22 destruct
+/2 width=1 by conj/
+qed-.
+
+lemma ist_inv_zero_shift: ∀c. 𝐓⦃0,↕*c⦄ → 𝐓⦃0,c⦄.
+#c #H elim (ist_inv_shift … H) -H //
+qed-.