update in ground_2, static_2, basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_shift.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_shift.ma
index e2f739d69572e6405257b51420dcff6dd05674d9..f5c00d822cbeb29bdf8b820d62273b6c3ff4e9ce 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_shift.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_shift.ma
@@ -12,20 +12,21 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/xoa/ex_5_4.ma".
 include "ground_2/notation/functions/updownarrowstar_1.ma".
-include "ground_2/steps/rtc_isrt.ma".
+include "ground_2/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〉 ].
+[ 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〉.
+lemma shift_rew: ∀ri,rs,ti,ts. 〈ri∨rs,0,ti∨ts,0〉 = ↕*〈ri,rs,ti,ts〉.
 normalize //
 qed.
 
@@ -34,27 +35,9 @@ lemma shift_O: 𝟘𝟘 = ↕*𝟘𝟘.
 
 (* Basic inversion properties ***********************************************)
 
-lemma shift_inv_dx: ∀ri,rs,ti,ts,c. 〈ri, rs, ti, ts〉 = ↕*c →
+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.
+                                       〈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-.
-
-(* Properties with test for costrained rt-transition counter ****************)
-
-lemma isr_shift: ∀c. 𝐑𝐓⦃0, c⦄ → 𝐑𝐓⦃0, ↕*c⦄.
-#c * #ri #rs #H destruct /2 width=3 by ex1_2_intro/
-qed.
-
-(* Inversion properties with test for costrained rt-counter *****************)
-
-lemma isrt_inv_shift: ∀n,c. 𝐑𝐓⦃n, ↕*c⦄ → 𝐑𝐓⦃0, c⦄ ∧ 0 = n.
-#n #c * #ri #rs #H
-elim (shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #_ #_ #H1 #H2 #H3
-elim (max_inv_O3 … H1) -H1 /3 width=3 by ex1_2_intro, conj/
-qed-.
-
-lemma isr_inv_shift: ∀c. 𝐑𝐓⦃0, ↕*c⦄ → 𝐑𝐓⦃0, c⦄.
-#c #H elim (isrt_inv_shift … H) -H //
-qed-.