Nuprl - Pf wp2 rel correct 1 1 1 2 1

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

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]] rho de e.state
13. x': [[A]] rho de e.state
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. rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr)
20. r@0: rel()
21. as: (LabelTerm) List
22. 1of(unzip(as)) = rel_primed_vars(r)
23. i:. i < ||as|| 2of(as[i]) (x.smts_eff(action_effect(kind(a);A.eff;A.frame);x))(1of(as[i]))
24. r@0 = rel_subst2(as;r)
25. value(a) [[dec_lookup(A.da;kind(a))]] rho

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]] rho de e.state
12. x': [[A]] rho de e.state
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. rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr)
19. r@0: rel()
20. as: (LabelTerm) List
21. 1of(unzip(as)) = rel_primed_vars(r)
22. i:. i < ||as|| 2of(as[i]) (x.smts_eff(action_effect(kind(a);A.eff;A.frame);x))(1of(as[i]))
23. r@0 = rel_subst2(as;r)
24. value(a) [[dec_lookup(A.da;kind(a))]] rho
25. 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