--- /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/notation/relations/istype_2.ma".
+include "ground/steps/rtc.ma".
+
+(* T-TRANSITION COUNTER *****************************************************)
+
+definition ist: relation2 nat rtc ≝
+ λts,c. 〈0,0,0,ts〉 = c.
+
+interpretation "test for t-transition counter (rtc)"
+ 'IsType ts c = (ist ts c).
+
+(* Basic properties *********************************************************)
+
+lemma ist_00: 𝐓❪0,𝟘𝟘❫.
+// qed.
+
+lemma ist_01: 𝐓❪1,𝟘𝟙❫.
+// qed.
+
+(* Basic inversion properties ***********************************************)
+
+lemma ist_inv_00: ∀n. 𝐓❪n,𝟘𝟘❫ → 0 = n.
+#n #H destruct //
+qed-.
+
+lemma ist_inv_01: ∀n. 𝐓❪n,𝟘𝟙❫ → 1 = n.
+#n #H destruct //
+qed-.
+
+lemma ist_inv_10: ∀n. 𝐓❪n,𝟙𝟘❫ → ⊥.
+#h #H destruct
+qed-.
+
+(* Main inversion properties ************************************************)
+
+theorem ist_inj: ∀n1,n2,c. 𝐓❪n1,c❫ → 𝐓❪n2,c❫ → n1 = n2.
+#n1 #n2 #c #H1 #H2 destruct //
+qed-.
+
+theorem ist_mono: ∀n,c1,c2. 𝐓❪n,c1❫ → 𝐓❪n,c2❫ → c1 = c2.
+#n #c1 #c2 #H1 #H2 destruct //
+qed-.