(* 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.
(* 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⦄.
+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.
+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⦄.
+lemma isr_inv_shift: ∀c. 𝐑𝐓⦃0,↕*c⦄ → 𝐑𝐓⦃0,c⦄.
#c #H elim (isrt_inv_shift … H) -H //
qed-.