ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / steps / rtc_shift.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/steps/rtc_shift.ma b/matita/matita/contribs/lambdadelta/ground/steps/rtc_shift.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/xoa/ex_5_4.ma".
+include "ground/notation/functions/updownarrowstar_1.ma".
+include "ground/steps/rtc.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+definition shift (c:rtc): rtc ≝ match c with
+[ mk_rtc ri rs ti ts ⇒ 〈ri∨rs,0,ti∨ts,0〉 ].
+
+interpretation "shift (rtc)"
+   'UpDownArrowStar c = (shift c).
+
+(* Basic properties *********************************************************)
+
+lemma shift_rew: ∀ri,rs,ti,ts. 〈ri∨rs,0,ti∨ts,0〉 = ↕*〈ri,rs,ti,ts〉.
+normalize //
+qed.
+
+lemma shift_O: 𝟘𝟘 = ↕*𝟘𝟘.
+// qed.
+
+(* Basic inversion properties ***********************************************)
+
+lemma shift_inv_dx: ∀ri,rs,ti,ts,c. 〈ri,rs,ti,ts〉 = ↕*c →
+                    ∃∃ri0,rs0,ti0,ts0. (ri0∨rs0) = ri & 0 = rs & (ti0∨ts0) = ti & 0 = ts &
+                                       〈ri0,rs0,ti0,ts0〉 = c.
+#ri #rs #ti #ts * #ri0 #rs0 #ti0 #ts0 <shift_rew #H destruct
+/2 width=7 by ex5_4_intro/
+qed-.