(* RT-TRANSITION COUNTER ****************************************************)
definition isrt: relation2 nat rtc ≝ λts,c.
- ∃∃ri,rs. 〈ri, rs, 0, ts〉 = c.
+ ∃∃ri,rs. 〈ri,rs,0,ts〉 = c.
interpretation "test for costrained rt-transition counter (rtc)"
'IsRedType ts c = (isrt ts c).
(* Basic properties *********************************************************)
-lemma isr_00: 𝐑𝐓⦃0, 𝟘𝟘⦄.
+lemma isrt_00: 𝐑𝐓❪0,𝟘𝟘❫.
/2 width=3 by ex1_2_intro/ qed.
-lemma isr_10: 𝐑𝐓⦃0, 𝟙𝟘⦄.
+lemma isrt_10: 𝐑𝐓❪0,𝟙𝟘❫.
/2 width=3 by ex1_2_intro/ qed.
-lemma isrt_01: ð\9d\90\91ð\9d\90\93â¦\831, ð\9d\9f\98ð\9d\9f\99â¦\84.
+lemma isrt_01: ð\9d\90\91ð\9d\90\93â\9dª1,ð\9d\9f\98ð\9d\9f\99â\9d«.
/2 width=3 by ex1_2_intro/ qed.
-lemma isrt_eq_t_trans: â\88\80n,c1,c2. ð\9d\90\91ð\9d\90\93â¦\83n, c1â¦\84 â\86\92 eq_t c1 c2 â\86\92 ð\9d\90\91ð\9d\90\93â¦\83n, c2â¦\84.
+lemma isrt_eq_t_trans: â\88\80n,c1,c2. ð\9d\90\91ð\9d\90\93â\9dªn,c1â\9d« â\86\92 eq_t c1 c2 â\86\92 ð\9d\90\91ð\9d\90\93â\9dªn,c2â\9d«.
#n #c1 #c2 * #ri1 #rs1 #H destruct
#H elim (eq_t_inv_dx … H) -H /2 width=3 by ex1_2_intro/
qed-.
(* Basic inversion properties ***********************************************)
-lemma isrt_inv_00: â\88\80n. ð\9d\90\91ð\9d\90\93â¦\83n, ð\9d\9f\98ð\9d\9f\98â¦\84 → 0 = n.
+lemma isrt_inv_00: â\88\80n. ð\9d\90\91ð\9d\90\93â\9dªn,ð\9d\9f\98ð\9d\9f\98â\9d« → 0 = n.
#n * #ri #rs #H destruct //
qed-.
-lemma isrt_inv_10: â\88\80n. ð\9d\90\91ð\9d\90\93â¦\83n, ð\9d\9f\99ð\9d\9f\98â¦\84 → 0 = n.
+lemma isrt_inv_10: â\88\80n. ð\9d\90\91ð\9d\90\93â\9dªn,ð\9d\9f\99ð\9d\9f\98â\9d« → 0 = n.
#n * #ri #rs #H destruct //
qed-.
-lemma isrt_inv_01: â\88\80n. ð\9d\90\91ð\9d\90\93â¦\83n, ð\9d\9f\98ð\9d\9f\99â¦\84 → 1 = n.
+lemma isrt_inv_01: â\88\80n. ð\9d\90\91ð\9d\90\93â\9dªn,ð\9d\9f\98ð\9d\9f\99â\9d« → 1 = n.
#n * #ri #rs #H destruct //
qed-.
(* Main inversion properties ************************************************)
-theorem isrt_inj: â\88\80n1,n2,c. ð\9d\90\91ð\9d\90\93â¦\83n1, câ¦\84 â\86\92 ð\9d\90\91ð\9d\90\93â¦\83n2, câ¦\84 → n1 = n2.
+theorem isrt_inj: â\88\80n1,n2,c. ð\9d\90\91ð\9d\90\93â\9dªn1,câ\9d« â\86\92 ð\9d\90\91ð\9d\90\93â\9dªn2,câ\9d« → n1 = n2.
#n1 #n2 #c * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct //
qed-.
-theorem isrt_mono: â\88\80n,c1,c2. ð\9d\90\91ð\9d\90\93â¦\83n, c1â¦\84 â\86\92 ð\9d\90\91ð\9d\90\93â¦\83n, c2â¦\84 → eq_t c1 c2.
+theorem isrt_mono: â\88\80n,c1,c2. ð\9d\90\91ð\9d\90\93â\9dªn,c1â\9d« â\86\92 ð\9d\90\91ð\9d\90\93â\9dªn,c2â\9d« → eq_t c1 c2.
#n #c1 #c2 * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct //
qed-.