some restyling ...

[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 a2746366cc458cf0f925767862f12d510a507fa1..165e1eeda586863948d44f2f2c2ab32a061ac84d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_shift.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_shift.ma
@@ -12,19 +12,49 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/functions/drop_1.ma".
-include "ground_2/steps/rtc.ma".
+include "ground_2/notation/functions/updownarrowstar_1.ma".
+include "ground_2/steps/rtc_isrt.ma".
 
 (* RT-TRANSITION COUNTER ****************************************************)
 
-definition shift (r:rtc): rtc ≝ match r with
-[ mk_rtc ri rh ti th ⇒ 〈ri+rh, 0, ti+th, 0〉 ].
+definition shift (c:rtc): rtc ≝ match c with
+[ mk_rtc ri rs ti ts ⇒ 〈ri∨rs,0,ti∨ts,0〉 ].
 
 interpretation "shift (rtc)"
-   'Drop r = (shift r).
+   'UpDownArrowStar c = (shift c).
 
 (* Basic properties *********************************************************)
 
-lemma shift_refl: ∀ri,ti. 〈ri, 0, ti, 0〉 = ↓〈ri, 0, ti, 0〉.
+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-.
+
+(* 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-.