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

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At: vc trace correct action decl lemma 1 1 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. 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. [[I]] rho A.ds < > de e x mk_trace_env(tr, te)
23. [[A]] rho de e.trans(x,act,x')
24. (t:dec(). t A.da & t.lbl = kind(act)) [[I]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
25. act ([[A.da]] rho)

[[wp(A;kind(act);I)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(mk_trace_env(tr, te);act) [[I]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)

By: (Inst Thm* A:ioa{i:l}(), de:sig(). tc_ioa(A;de) ioa_mentions_trace(A) (Q:Fmla, rho:Decl, e:{[[de]] rho}, a:[[A]] rho de e.action, tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;tr.proj;Q) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc_pred(Q;A.ds; < > ;de) closed_pred(Q) covers_pred(A;Q) [[A]] rho de e.trans(s,a,x') ([[Q]] rho A.ds < > de e x' tr [[wp(A;kind(a);Q)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))) [A;de;I;rho;e;act;tappend(mk_trace_env(tr, te);act);x;x']) THENA (Auto THEN TrivialIoaHyp THEN (Unfold `tappend` 0) THEN (Reduce 0)) THEN Analyze -1 THEN Try Trivial

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