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

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

At: vc trace correct action decl lemma 1 2 1 1 2 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. (t:dec(). t A.da & t.lbl = kind(act)) (r:rel(). r I [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act))
25. (r:rel(). (r@0:rel(). r@0 I & r smts_eff_rel( < e.smt | e < e A.eff | e.kind = kind(act) > > + < mk_smt(f.var, f.var, f.typ) | f < f A.frame | kind(act) f.acts > > ;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))
26. r: rel()
27. r I
28. act ([[A.da]] rho)
29. [[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)

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

By: Analyze -1 THEN Analyze -1

Generated subgoals:

1 29. [[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)
[[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(mk_trace_env(tr, te);act)

2 29. [[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)
30. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
[[r]] rho A.ds < > de e x' mk_trace_env(tr @ [act], te)

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

1	29. `[[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)` `[[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) tappend(mk_trace_env(tr, te);act)`
2	29. `[[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)` 30. `[[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)` `[[r]] rho A.ds < > de e x' mk_trace_env(tr @ [act], te)`