Nuprl - Pf wp correctness 1 2 2 2 2

(27steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc

1. A: ioa{i:l}()
2. de: sig()
3. tc_ioa(A;de)
4. ioa_mentions_trace(A)
5. Q: Fmla
6. rho: Decl
7. e: {[[de]] rho}
8. a: [[A]] rho de e.action
9. tr: trace_env([[A.da]] rho)
10. tc_ioa(A;de)
11. ioa_mentions_trace(A)
12. trace_consistent_pred(rho;A.da;tr.proj;Q)
13. single_valued_decls(A.ds)
14. s: [[A]] rho de e.state
15. x': [[A]] rho de e.state
16. tc_pred(Q;A.ds; < > ;de)
17. closed_pred(Q)
18. covers_pred(A;Q)
19. [[A]] rho de e.trans(s,a,x')
20. pred_mng_2((Q)'; rho; A.ds; < > ; de; e; s; x'; ; tr) [[wp2(A;kind(a);(Q)')]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr
21. [[wp2(A;kind(a);(Q)')]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr Prop
22. pred_mng_2((Q)'; rho; A.ds; < > ; de; e; s; x'; ; tr) Prop
23. [[wp(A;kind(a);Q)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr Prop
24. [[Q]] rho A.ds < > de e x' tr Prop

[[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

By: (Inst Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) (pred_mng_2((p)'; rho; ds; da; de; e; s; s'; a; tr) [[p]] rho ds da de e s' a tr) [Q;A.ds;A.da; < > ;de;rho;e;s;x';;tr]) THENA (Try (Complete (Auto THEN TrivialIoaHyp THEN (Try (BackThru Thm* v:Top, rho:Decl. v [[ < > ]] rho)))))

Generated subgoal:

1 25. pred_mng_2((Q)'; rho; A.ds; < > ; de; e; s; x'; ; tr) [[Q]] rho A.ds < > de e x' tr
[[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

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(27steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc