Step
*
2
1
1
1
1
1
of Lemma
pRun2_wf
1. M : Type ─→ Type
2. M[Top]
3. ∀P:Type. value-type(M[P])
4. Continuous+(P.M[P])
5. nat2msg : ℕ ─→ pMsg(P.M[P])
6. loc2msg : Id ─→ pMsg(P.M[P])
7. S0 : System(P.M[P])
8. env : pEnvType(P.M[P])
9. t : {1...}
10. ∀t:ℕt
(pRun2(S0;env;nat2msg;loc2msg;t) ∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = (t + 1) ∈ ℤ} )
11. pRun2(S0;env;nat2msg;loc2msg;t - 1) ∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List|
||L|| = ((t - 1) + 1) ∈ ℤ}
12. v : {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = ((t - 1) + 1) ∈ ℤ} @i
13. pRun2(S0;env;nat2msg;loc2msg;t - 1)
= v
∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = ((t - 1) + 1) ∈ ℤ} @i
14. v2 : ℕ@i
15. v4 : ℕ@i
16. v5 : Id@i
17. (env t (λi.v[i])) = <v2, v4, v5> ∈ (ℕ × ℕ × Id)@i
18. v7 : ℤ × Id × Id × pMsg(P.M[P])?@i
19. v8 : System(P.M[P])@i
20. do-chosen-command(nat2msg;loc2msg;t;snd(last(v));v2;v4;v5)
= <v7, v8>
∈ (ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P]))@i
21. norm-runinfo(v7) ∈ {info':pRunInfo(P.M[P])| info' = v7 ∈ pRunInfo(P.M[P])}
22. v9 : {info':pRunInfo(P.M[P])| info' = v7 ∈ pRunInfo(P.M[P])} @i
23. norm-runinfo(v7) = v9 ∈ {info':pRunInfo(P.M[P])| info' = v7 ∈ pRunInfo(P.M[P])} @i
⊢ (v9)↓
BY
{ D -2 }
1
1. M : Type ─→ Type
2. M[Top]
3. ∀P:Type. value-type(M[P])
4. Continuous+(P.M[P])
5. nat2msg : ℕ ─→ pMsg(P.M[P])
6. loc2msg : Id ─→ pMsg(P.M[P])
7. S0 : System(P.M[P])
8. env : pEnvType(P.M[P])
9. t : {1...}
10. ∀t:ℕt
(pRun2(S0;env;nat2msg;loc2msg;t) ∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = (t + 1) ∈ ℤ} )
11. pRun2(S0;env;nat2msg;loc2msg;t - 1) ∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List|
||L|| = ((t - 1) + 1) ∈ ℤ}
12. v : {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = ((t - 1) + 1) ∈ ℤ} @i
13. pRun2(S0;env;nat2msg;loc2msg;t - 1)
= v
∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = ((t - 1) + 1) ∈ ℤ} @i
14. v2 : ℕ@i
15. v4 : ℕ@i
16. v5 : Id@i
17. (env t (λi.v[i])) = <v2, v4, v5> ∈ (ℕ × ℕ × Id)@i
18. v7 : ℤ × Id × Id × pMsg(P.M[P])?@i
19. v8 : System(P.M[P])@i
20. do-chosen-command(nat2msg;loc2msg;t;snd(last(v));v2;v4;v5)
= <v7, v8>
∈ (ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P]))@i
21. norm-runinfo(v7) ∈ {info':pRunInfo(P.M[P])| info' = v7 ∈ pRunInfo(P.M[P])}
22. v9 : pRunInfo(P.M[P])@i
23. \\%29 : v9 = v7 ∈ pRunInfo(P.M[P])@i
24. norm-runinfo(v7) = v9 ∈ {info':pRunInfo(P.M[P])| info' = v7 ∈ pRunInfo(P.M[P])} @i
⊢ (v9)↓
Latex:
Latex:
1. M : Type {}\mrightarrow{} Type
2. M[Top]
3. \mforall{}P:Type. value-type(M[P])
4. Continuous+(P.M[P])
5. nat2msg : \mBbbN{} {}\mrightarrow{} pMsg(P.M[P])
6. loc2msg : Id {}\mrightarrow{} pMsg(P.M[P])
7. S0 : System(P.M[P])
8. env : pEnvType(P.M[P])
9. t : \{1...\}
10. \mforall{}t:\mBbbN{}t
(pRun2(S0;env;nat2msg;loc2msg;t) \mmember{} \{L:(\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P])) List|
||L|| = (t + 1)\} )
11. pRun2(S0;env;nat2msg;loc2msg;t - 1) \mmember{} \{L:(\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P])) List|
||L|| = ((t - 1) + 1)\}
12. v : \{L:(\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P])) List| ||L|| = ((t - 1) + 1)\} @i
13. pRun2(S0;env;nat2msg;loc2msg;t - 1) = v@i
14. v2 : \mBbbN{}@i
15. v4 : \mBbbN{}@i
16. v5 : Id@i
17. (env t (\mlambda{}i.v[i])) = <v2, v4, v5>@i
18. v7 : \mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])?@i
19. v8 : System(P.M[P])@i
20. do-chosen-command(nat2msg;loc2msg;t;snd(last(v));v2;v4;v5) = <v7, v8>@i
21. norm-runinfo(v7) \mmember{} \{info':pRunInfo(P.M[P])| info' = v7\}
22. v9 : \{info':pRunInfo(P.M[P])| info' = v7\} @i
23. norm-runinfo(v7) = v9@i
\mvdash{} (v9)\mdownarrow{}
By
Latex:
D -2
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