matita/matita/contribs/lambdadelta/ground/steps/rtc_shift.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/xoa/ex_5_4.ma".
  16 include "ground/notation/functions/updownarrowstar_1.ma".
  17 include "ground/steps/rtc.ma".
  18
  19 (* RT-TRANSITION COUNTER ****************************************************)
  20
  21 definition shift (c:rtc): rtc ≝ match c with
  22 [ mk_rtc ri rs ti ts ⇒ 〈ri∨rs,0,ti∨ts,0〉 ].
  23
  24 interpretation "shift (rtc)"
  25    'UpDownArrowStar c = (shift c).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma shift_rew: ∀ri,rs,ti,ts. 〈ri∨rs,0,ti∨ts,0〉 = ↕*〈ri,rs,ti,ts〉.
  30 normalize //
  31 qed.
  32
  33 lemma shift_O: 𝟘𝟘 = ↕*𝟘𝟘.
  34 // qed.
  35
  36 (* Basic inversion properties ***********************************************)
  37
  38 lemma shift_inv_dx: ∀ri,rs,ti,ts,c. 〈ri,rs,ti,ts〉 = ↕*c →
  39                     ∃∃ri0,rs0,ti0,ts0. (ri0∨rs0) = ri & 0 = rs & (ti0∨ts0) = ti & 0 = ts &
  40                                        〈ri0,rs0,ti0,ts0〉 = c.
  41 #ri #rs #ti #ts * #ri0 #rs0 #ti0 #ts0 <shift_rew #H destruct
  42 /2 width=7 by ex5_4_intro/
  43 qed-.