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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground_2/steps/rtc_max.ma".
16 include "ground_2/steps/rtc_ist.ma".
18 (* RT-TRANSITION COUNTER ****************************************************)
20 (* Properties with test for t-transition counter ****************************)
22 lemma ist_max: ∀n1,n2,c1,c2. 𝐓⦃n1,c1⦄ → 𝐓⦃n2,c2⦄ → 𝐓⦃n1∨n2,c1∨c2⦄.
23 #n1 #n2 #c1 #c2 #H1 #H2 destruct //
26 lemma ist_max_O1: ∀n,c1,c2. 𝐓⦃0,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1∨c2⦄.
27 /2 width=1 by ist_max/ qed.
29 lemma ist_max_O2: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1∨c2⦄.
30 #n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by ist_max/
33 lemma ist_max_idem1: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1∨c2⦄.
34 #n #c1 #c2 #H1 #H2 >(idempotent_max n) /2 width=1 by ist_max/
37 (* Inversion properties with test for t-transition counter ******************)
40 ∀n,c1,c2. 𝐓⦃n,c1 ∨ c2⦄ →
41 ∃∃n1,n2. 𝐓⦃n1,c1⦄ & 𝐓⦃n2,c2⦄ & (n1 ∨ n2) = n.
43 elim (max_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct
44 elim (max_inv_O3 … H1) -H1 #H11 #H12 destruct
45 elim (max_inv_O3 … H2) -H2 #H21 #H22 destruct
46 elim (max_inv_O3 … H3) -H3 #H31 #H32 destruct
47 /2 width=5 by ex3_2_intro/
50 lemma ist_O_inv_max: ∀c1,c2. 𝐓⦃0,c1 ∨ c2⦄ → ∧∧ 𝐓⦃0,c1⦄ & 𝐓⦃0,c2⦄.
52 elim (ist_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H
53 elim (max_inv_O3 … H) -H #H1 #H2 destruct
57 lemma ist_inv_max_O_dx: ∀n,c1,c2. 𝐓⦃n,c1 ∨ c2⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1⦄.
59 elim (ist_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //