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

At: vc trace correct action decl lemma 1 2 1 1 2 2 1 1 1 2 2 1 1
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. (r:rel(). (r@0:rel(). r@0 I & r wp_rel(A;kind(act);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))
25. r: rel()
26. r I
27. act ([[A.da]] rho)
28. [[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)
29. r@0: rel()
30. r@0 smts_eff_rel(action_effect(kind(act);A.eff;A.frame);r)
31. rel_eq(rel_unprime(r@0);rel_unprime(r))
32. r:rel(). r I [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)
33. [[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(mk_trace_env(tr, te);act)
By:
(Inst Thm* A:ioa{i:l}(), r:rel(), rho:Decl, de:sig(), e:{[[de]] rho}, a:([[A.da]] rho), tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_rel(rho;A.da;tr.proj;r) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc(r;A.ds; < > ;de) closed_rel(r) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') ([[r]] rho A.ds < > de e x' tr [[wp_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr)) [A;r;rho;de;e;act;tappend(mk_trace_env(tr, te);act);x;x']) THENA (Auto THEN TrivialIoaHyp)
THEN
Try ((Unfold `tappend` 0) THEN (Reduce 0))
THEN
EasyHypThen Auto
Generated subgoals:

1 covers_rel(A;r)
234. [[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)
35. [[r]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act) [[wp_rel(A;kind(act);r)]] rho ... ... de e x ... ...
[[wp_rel(A;kind(act);r)]] rho A.ds dec_lookup(A.da;kind(act)) de e x value(act) mk_trace_env(tr @ [act], te)

About:
listconsnilboolassertitapplyfunction
memberimpliesandallexists

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