Nuprl - Pf vc trace correct action decl lemma 1 2 1 1 2 2 1 1 1 2 2 1 1 2

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At: vc trace correct action decl lemma 1 2 1 1 2 2 1 1 1 2 2 1 1 2

1. A: ioa{i:l}()
2. I: Collection(rel())
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. tc_pred(I;A.ds; < > ;de)
11. covers_pred(A;I)
12. guarded_trace(A.da;te;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. tr: ([[A.da]] rho) List
20. [[A]] rho de e.init(s0)
21. trace_reachable([[A]] rho de e;s0;mk_trace_env(tr, te).trace;x)
22. r:rel(). r I [[r]] rho A.ds < > de e x mk_trace_env(tr, te)
23. [[A]] rho de e.trans(x,act,x')
24. (r:rel(). (r@0:rel(). r@0 I & r wp_rel(A;kind(act);r@0)) [[r]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(mk_trace_env(tr, te);act)) (r:rel(). r I [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act))
25. r: rel()
26. r I
27. act ([[A.da]] rho)
28. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act) [[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(...;act)
29. r@0: rel()
30. r@0 smts_eff_rel(action_effect(kind(act);A.eff;A.frame);r)
31. rel_eq(rel_unprime(r@0);rel_unprime(r))
32. r:rel(). r I [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
33. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
34. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act) [[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(...;act)
35. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act) [[wp_rel(A;kind(act);r)]] rho ... ... de e x ... ...

[[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) mk_trace_env(tr @ [act], te)

By: ThinTrivial

Generated subgoal:

1 28. r@0: rel()
29. r@0 smts_eff_rel(action_effect(kind(act);A.eff;A.frame);r)
30. rel_eq(rel_unprime(r@0);rel_unprime(r))
31. r:rel(). r I [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
32. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
33. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act) [[wp_rel(A;kind(act);r)]] rho ... ... de e x ... ...
34. [[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(...;act)
35. [[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(...;act)
[[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) mk_trace_env(tr @ [act], te)

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