Nuprl - Pf wp2 rel correct 2 1 2 1 1 1 2 2 1 1 2

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At: wp2 rel correct 2 1 2 1 1 1 2 2 1 1 2

1. A: ioa{i:l}()
2. r: rel()
3. rho: Decl
4. de: sig()
5. e: {[[de]] rho}
6. a: ([[A.da]] rho)
7. tr: trace_env([[A.da]] rho)
8. tc_ioa(A;de)
9. ioa_mentions_trace(A)
10. trace_consistent_rel(rho;A.da;tr.proj;r)
11. single_valued_decls(A.ds)
12. s: {[[A.ds]] rho}
13. x': {[[A.ds]] rho}
14. tc(r;A.ds;dec_lookup(A.da;kind(a));de)
15. covers_rel(A;r)
16. p:pre(). p A.pre p.kind = kind(a) [[p.rel]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) niltrace()
17. ef:eff(). ef A.eff ef.kind = kind(a) x'.ef.smt.lbl = [[ef.smt.term]] 1of(e) s value(a) niltrace() [[ef.smt.typ]] rho
18. fr:frame(). fr A.frame (kind(a) fr.acts) x'.fr.var = s.fr.var [[fr.typ]] rho
19. x:Label. rel_mentions(r;x) covers_var(A;x)
20. value(a) [[dec_lookup(A.da;kind(a))]] rho
21. r@0:rel(). r@0 col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r) [[r@0]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr
22. r': rel()
23. as: (LabelTerm) List
24. 1of(unzip(as)) = rel_primed_vars(r)
25. i:. i < ||as|| 2of(as[i]) smts_eff(action_effect(kind(a);A.eff;A.frame);1of(as[i]))
26. r' = rel_subst2(as;r)
27. tc(r;A.ds;dec_lookup(A.da;kind(a));de)

x:Label. (x rel_primed_vars(r)) (t:SimpleType. mk_dec(x, t) A.ds t term_types(A.ds;dec_lookup(A.da;kind(a));de;apply_alist(as;x;x)) & x'.x = [[apply_alist(as;x;x)]] 1of(e) s value(a) tr [[t]] rho)

By: MoveToHyp -10 -1 THEN RevHypSubstSq -3 0 THEN Analyze 0 THEN Analyze 0 THEN Inst Thm* as:(LabelT) List, d:T, x:Label. (x 1of(unzip(as))) ( < x,apply_alist(as;x;d) > as) [Term;as;x;x] THEN Unfold `l_member` -1 THEN Reduce -1 THEN ExRepDHyps THEN Subst (apply_alist(as;x;x) ~ 2of(as[i])) 0 THEN Subst (x ~ 1of(as[i])) 0 THEN Try (Auto THEN (RevHypSubst -1 0) THEN (Reduce 0) THEN (Complete Auto)) THEN AllHyps (i.(InstHyp [i] i) THENA (Complete Auto)) THEN Reduce -1 THEN MoveToConcl -1 THEN GenConcl (2of(as[i]) = xxx) THEN GenConcl (1of(as[i]) = xx) THEN Analyze 0

Generated subgoal:

1 18. tc(r;A.ds;dec_lookup(A.da;kind(a));de)
19. fr:frame(). fr A.frame (kind(a) fr.acts) x'.fr.var = s.fr.var [[fr.typ]] rho
20. x:Label. rel_mentions(r;x) covers_var(A;x)
21. value(a) [[dec_lookup(A.da;kind(a))]] rho
22. r@0:rel(). r@0 col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r) [[r@0]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr
23. r': rel()
24. as: (LabelTerm) List
25. 1of(unzip(as)) = rel_primed_vars(r)
26. i:. i < ||as|| 2of(as[i]) smts_eff(action_effect(kind(a);A.eff;A.frame);1of(as[i]))
27. r' = rel_subst2(as;r)
28. x: Label
29. (x 1of(unzip(as)))
30. i:
31. i < ||as||
32. < x,apply_alist(as;x;x) > = as[i]
33. xxx: Term
34. 2of(as[i]) = xxx
35. xx: Label
36. 1of(as[i]) = xx
37. xxx smts_eff(action_effect(kind(a);A.eff;A.frame);xx)
t:SimpleType. mk_dec(xx, t) A.ds t term_types(A.ds;dec_lookup(A.da;kind(a));de;xxx) & x'.xx = [[xxx]] 1of(e) s value(a) tr [[t]] rho

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(73steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc