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

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

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. [[I]] rho A.ds < > de e x mk_trace_env(l, te)
24. [[A]] rho de e.trans(x,act,x')
25. l ([[A.da]] rho) List
26. [[VCs(A;I)]] rho A.ds A.da de e x mk_trace_env(l, te)
27. act ([[A.da]] rho)
28. (t:dec(). t A.da & t.lbl = kind(act)) [[I]] rho A.ds < > de e x' mk_trace_env(l @ [act], te)

[[I]] rho A.ds < > de e x' mk_trace_env(l @ [act], te)

By: (Inst Thm* A:ioa{i:l}(), I:Fmla, rho:Decl, de:sig(), e:{[[de]] rho}, te:(LabelLabel). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;te;I) tc_pred(I;A.ds; < > ;de) covers_pred(A;I) guarded_trace(A.da;te;I) closed_pred(I) single_valued_decls(A.ds) (s0,x:[[A]] rho de e.state, act:[[A]] rho de e.action, x':[[A]] rho de e.state, tr:([[A.da]] rho) List. [[A]] rho de e.init(s0) trace_reachable([[A]] rho de e;s0;mk_trace_env(tr, te).trace;x) [[I]] rho A.ds < > de e x mk_trace_env(tr, te) [[A]] rho de e.trans(x,act,x') ((t:dec(). t A.da & t.lbl = kind(act)) [[I]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)) [[I]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)) [A;I;rho;de;e;te;s0;x;act;x';l]) THENA (Auto THEN (Reduce 0)) THEN ThinTrivial THEN All (h.(Unfold `tappend` h) THEN (Reduce h) THEN Trivial)

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