--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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_isrt.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+(* Properties with test for costrained rt-transition counter ****************)
+
+lemma isr_shift: âc. ððâŠ0,câŦ â ððâŠ0,â*câŦ.
+#c * #ri #rs #H destruct /2 width=3 by ex1_2_intro/
+qed.
+
+(* Inversion properties with test for costrained rt-counter *****************)
+
+lemma isrt_inv_shift: ân,c. ððâŠn,â*câŦ â ððâŠ0,câŦ ⧠0 = n.
+#n #c * #ri #rs #H
+elim (shift_inv_dx âĶ H) -H #rt0 #rs0 #ti0 #ts0 #_ #_ #H1 #H2 #H3
+elim (max_inv_O3 âĶ H1) -H1 /3 width=3 by ex1_2_intro, conj/
+qed-.
+
+lemma isr_inv_shift: âc. ððâŠ0,â*câŦ â ððâŠ0,câŦ.
+#c #H elim (isrt_inv_shift âĶ H) -H //
+qed-.