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

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

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)

subst_mentions_trace(as)

By: AllHyps (h.(Unfold `ioa_mentions_trace` h) THEN (ParallelOp h)) THEN RepeatFor 2 OrLeft

Generated subgoal:

1 9. trace_consistent_rel(rho;A.da;tr.proj;r)
10. single_valued_decls(A.ds)
11. s: {[[A.ds]] rho}
12. x': {[[A.ds]] rho}
13. tc(r;A.ds;dec_lookup(A.da;kind(a));de)
14. covers_rel(A;r)
15. 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()
16. 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
17. fr:frame(). fr A.frame (kind(a) fr.acts) x'.fr.var = s.fr.var [[fr.typ]] rho
18. x:Label. rel_mentions(r;x) covers_var(A;x)
19. value(a) [[dec_lookup(A.da;kind(a))]] rho
20. 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
21. r': rel()
22. as: (LabelTerm) List
23. 1of(unzip(as)) = rel_primed_vars(r)
24. i:. i < ||as|| 2of(as[i]) smts_eff(action_effect(kind(a);A.eff;A.frame);1of(as[i]))
25. r' = rel_subst2(as;r)
26. tc(r;A.ds;dec_lookup(A.da;kind(a));de)
27. subst_mentions_trace(as)
e:eff(). e A.eff & mentions_trace(e.smt.term)

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