propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / counters / rtc_ist.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/counters/rtc_ist.ma b/matita/matita/contribs/lambdadelta/ground/counters/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/notation/relations/ist_2.ma".
+include "ground/counters/rtc.ma".
+
+(* T-TRANSITION COUNTERS ****************************************************)
+
+definition rtc_ist: relation2 nat rtc ≝
+           λts,c. 〈𝟎,𝟎,𝟎,ts〉 = c.
+
+interpretation
+  "t-transition counters (rtc)"
+  'IsT ts c = (rtc_ist ts c).
+
+(* Basic constructions ******************************************************)
+
+lemma rtc_ist_zz: 𝐓❪𝟎,𝟘𝟘❫.
+// qed.
+
+lemma rtc_ist_zu: 𝐓❪𝟏,𝟘𝟙❫.
+// qed.
+
+(* Basic inversions *********************************************************)
+
+lemma rtc_ist_inv_zz (n): 𝐓❪n,𝟘𝟘❫ → 𝟎 = n.
+#n #H destruct //
+qed-.
+
+lemma rtc_ist_inv_zu (n): 𝐓❪n,𝟘𝟙❫ → ninj (𝟏) = n.
+#n #H destruct //
+qed-.
+
+lemma rtc_ist_inv_uz (n): 𝐓❪n,𝟙𝟘❫ → ⊥.
+#h #H destruct
+qed-.
+
+(* Main inversions **********************************************************)
+
+theorem rtc_ist_inj (n1) (n2) (c): 𝐓❪n1,c❫ → 𝐓❪n2,c❫ → n1 = n2.
+#n1 #n2 #c #H1 #H2 destruct //
+qed-.
+
+theorem rtc_ist_mono (n) (c1) (c2): 𝐓❪n,c1❫ → 𝐓❪n,c2❫ → c1 = c2.
+#n #c1 #c2 #H1 #H2 destruct //
+qed-.