--- /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/xoa/ex_5_4.ma".
+include "ground/notation/functions/updownarrowstar_1.ma".
+include "ground/arith/nat_max.ma".
+include "ground/counters/rtc.ma".
+
+(* SHIFT FOR RT-TRANSITION COUNTERS *****************************************)
+
+definition rtc_shift (c:rtc): rtc β
+match c with
+[ mk_rtc ri rs ti ts β β©ri β¨ rs, π, ti β¨ ts, πβͺ
+].
+
+interpretation
+ "shift (rtc)"
+ 'UpDownArrowStar c = (rtc_shift c).
+
+(* Basic constructions ******************************************************)
+
+lemma rtc_shift_rew (ri) (rs) (ti) (ts):
+ β©ri β¨ rs, π, ti β¨ ts, πβͺ = β*β©ri,rs,ti,tsβͺ.
+//
+qed.
+
+lemma rtc_shift_zz: ππ = β*ππ.
+// qed.
+
+(* Basic inversions *********************************************************)
+
+lemma rtc_shift_inv_dx (ri) (rs) (ti) (ts) (c):
+ β©ri,rs,ti,tsβͺ = β*c β
+ ββri0,rs0,ti0,ts0.
+ (ri0β¨rs0) = ri & π = rs & (ti0β¨ts0) = ti & π = ts & β©ri0,rs0,ti0,ts0βͺ = c.
+#ri #rs #ti #ts * #ri0 #rs0 #ti0 #ts0 <rtc_shift_rew #H destruct
+/2 width=7 by ex5_4_intro/
+qed-.