update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / steps / rtc_ist.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist.ma
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+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist.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/notation/relations/istype_2.ma".
+include "ground_2/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 isr_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-.
+
+(* 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-.