Nuprl - Pf vc trace correctness 1 3 2 1 2 2 2 1 1 1 1 1 1 1 2 2 1 2 1

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At: vc trace correctness 1 3 2 1 2 2 2 1 1 1 1 1 1 1 2 2 1 2 1

1. A: ioa{i:l}()
2. I: Fmla
3. rho: Decl
4. de: sig()
5. e: {[[de]] rho}
6. te: LabelLabel
7. tc_ioa(A;de)
8. ioa_mentions_trace(A)
9. trace_consistent_pred(rho;A.da;te;I)
10. guarded_trace(A.da;te;I)
11. tc_pred(I;A.ds; < > ;de)
12. covers_pred(A;I)
13. closed_pred(I)
14. single_valued_decls(A.ds)
15. s0: [[A]] rho de e.state
16. x: [[A]] rho de e.state
17. act: [[A]] rho de e.action
18. x': [[A]] rho de e.state
19. l: [[A]] rho de e.action List
20. [[A]] rho de e.init(s0)
21. trace_reachable([[A]] rho de e;s0;l;x)
22. mk_trace_env(l, te) trace_env([[A.da]] rho)
23. t: dec()
24. t A.da
25. t.lbl = kind(act)
26. [[I]] rho A.ds < > de e x mk_trace_env(l, te)
27. [[A]] rho de e.trans(x,act,x')
28. l ([[A.da]] rho) List
29. v:vc{i:l}(). v < *vc_imp(mk_imp(A.init, I))* > (a:dec(). a A.da & v = ioa_trans(A;a.lbl;I)) vc_mng(v;rho;A.ds;A.da;de;e;x;mk_trace_env(l, te))
30. act ([[A.da]] rho)
31. v:[[dec_lookup(A.da;kind(act))]] rho. [[I action_pre(kind(act);A.pre)]] rho A.ds dec_lookup(A.da;kind(act)) de e x v mk_trace_env(l, te) [[wp(A;kind(act);I)]] rho A.ds dec_lookup(A.da;kind(act)) de e x v tappend(mk_trace_env(l, te); < kind(act),v > )
32. r: rel()
33. p: pre()
34. p A.pre
35. p.kind = kind(act)
36. r = p.rel
37. p.kind = kind(act)

[[p.rel]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) mk_trace_env(l, te)

By: AllHyps (h. (Unfold `ioa_mng` h) THEN (Reduce h) THEN ExRepD THEN (InstHyp [p] h) THEN (NthHypSq -1) THEN (BackThru Thm* r:rel(), rho,ds,da,de,e,s,a,tr,tr':Top. rel_mentions_trace(r) ([[r]] rho ds da de e s a tr' ~ [[r]] rho ds da de e s a tr)))

Generated subgoal:

1 27. p:pre(). p A.pre p.kind = kind(act) [[p.rel]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) niltrace()
28. ef:eff(). ef A.eff ef.kind = kind(act) x'.ef.smt.lbl = [[ef.smt.term]] 1of(e) x value(act) niltrace() [[ef.smt.typ]] rho
29. fr:frame(). fr A.frame (kind(act) fr.acts) x'.fr.var = x.fr.var [[fr.typ]] rho
30. l ([[A.da]] rho) List
31. v:vc{i:l}(). v < *vc_imp(mk_imp(A.init, I))* > (a:dec(). a A.da & v = ioa_trans(A;a.lbl;I)) vc_mng(v;rho;A.ds;A.da;de;e;x;mk_trace_env(l, te))
32. act ([[A.da]] rho)
33. v:[[dec_lookup(A.da;kind(act))]] rho. [[I action_pre(kind(act);A.pre)]] rho A.ds dec_lookup(A.da;kind(act)) de e x v mk_trace_env(l, te) [[wp(A;kind(act);I)]] rho A.ds dec_lookup(A.da;kind(act)) de e x v tappend(mk_trace_env(l, te); < kind(act),v > )
34. r: rel()
35. p: pre()
36. p A.pre
37. p.kind = kind(act)
38. r = p.rel
39. p.kind = kind(act)
40. [[p.rel]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) niltrace()
rel_mentions_trace(p.rel)

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(51steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc