(* 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 isr_00: 𝐑𝐓⦃0,𝟘𝟘⦄.
/2 width=3 by ex1_2_intro/ qed.
-lemma isr_10: 𝐑𝐓⦃0, 𝟙𝟘⦄.
+lemma isr_10: 𝐑𝐓⦃0,𝟙𝟘⦄.
/2 width=3 by ex1_2_intro/ qed.
-lemma isrt_01: 𝐑𝐓⦃1, 𝟘𝟙⦄.
+lemma isrt_01: 𝐑𝐓⦃1,𝟘𝟙⦄.
/2 width=3 by ex1_2_intro/ qed.
-lemma isrt_eq_t_trans: ∀n,c1,c2. 𝐑𝐓⦃n, c1⦄ → eq_t c1 c2 → 𝐑𝐓⦃n, c2⦄.
+lemma isrt_eq_t_trans: ∀n,c1,c2. 𝐑𝐓⦃n,c1⦄ → eq_t c1 c2 → 𝐑𝐓⦃n,c2⦄.
#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: ∀n. 𝐑𝐓⦃n, 𝟘𝟘⦄ → 0 = n.
+lemma isrt_inv_00: ∀n. 𝐑𝐓⦃n,𝟘𝟘⦄ → 0 = n.
#n * #ri #rs #H destruct //
qed-.
-lemma isrt_inv_10: ∀n. 𝐑𝐓⦃n, 𝟙𝟘⦄ → 0 = n.
+lemma isrt_inv_10: ∀n. 𝐑𝐓⦃n,𝟙𝟘⦄ → 0 = n.
#n * #ri #rs #H destruct //
qed-.
-lemma isrt_inv_01: ∀n. 𝐑𝐓⦃n, 𝟘𝟙⦄ → 1 = n.
+lemma isrt_inv_01: ∀n. 𝐑𝐓⦃n,𝟘𝟙⦄ → 1 = n.
#n * #ri #rs #H destruct //
qed-.
(* Main inversion properties ************************************************)
-theorem isrt_inj: ∀n1,n2,c. 𝐑𝐓⦃n1, c⦄ → 𝐑𝐓⦃n2, c⦄ → n1 = n2.
+theorem isrt_inj: ∀n1,n2,c. 𝐑𝐓⦃n1,c⦄ → 𝐑𝐓⦃n2,c⦄ → n1 = n2.
#n1 #n2 #c * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct //
qed-.
-theorem isrt_mono: ∀n,c1,c2. 𝐑𝐓⦃n, c1⦄ → 𝐑𝐓⦃n, c2⦄ → eq_t c1 c2.
+theorem isrt_mono: ∀n,c1,c2. 𝐑𝐓⦃n,c1⦄ → 𝐑𝐓⦃n,c2⦄ → eq_t c1 c2.
#n #c1 #c2 * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct //
qed-.