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

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

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. s:[[A]] rho de e.state, tr:([[A.da]] rho) List. ([[A]] rho de e -tr- > s) [[VCs(A;I)]] rho A.ds A.da de e s mk_trace_env(tr, te)
16. x: [[A]] rho de e.state
17. [[A]] rho de e.init(x)
18. v:vc{i:l}(). v < *vc_imp(mk_imp(A.init, I))* > +* ioa_trans_all{i}(A;I) vc_mng(v;rho;A.ds;A.da;de;e;x;mk_trace_env(nil, te))
19. [[A.init]] rho A.ds < > de e x mk_trace_env(nil, te) [[I]] rho A.ds < > de e x mk_trace_env(nil, te)

[[A.init]] rho A.ds < > de e x mk_trace_env(nil, te)

By: Unfold `ioa_mng` -3 THEN Reduce -3 THEN RepeatFor 2 (ParallelOp -3) THEN ParallelOp -1

Generated subgoal:

1 17. r:rel(). r A.init [[r]] rho A.ds < > de e x niltrace()
18. v:vc{i:l}(). v < *vc_imp(mk_imp(A.init, I))* > +* ioa_trans_all{i}(A;I) vc_mng(v;rho;A.ds;A.da;de;e;x;mk_trace_env(nil, te))
19. [[A.init]] rho A.ds < > de e x mk_trace_env(nil, te) [[I]] rho A.ds < > de e x mk_trace_env(nil, te)
20. r: rel()
21. r A.init
22. [[r]] rho A.ds < > de e x niltrace()
[[r]] rho A.ds < > de e x mk_trace_env(nil, te)

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