Nuprl - Pf wp2 rel correct 1 1 1 2 2 1 2 1 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. value(a) [[dec_lookup(A.da;kind(a))]] rho
17. 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()
18. 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
19. fr:frame(). fr A.frame (kind(a) fr.acts) x'.fr.var = s.fr.var [[fr.typ]] rho
20. rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr)
21. r@0: rel()
22. as: (LabelTerm) List
23. 1of(unzip(as)) = rel_primed_vars(r)
24. i:. i < ||as|| 2of(as[i]) (x.smts_eff(action_effect(kind(a);A.eff;A.frame);x))(1of(as[i]))
25. r@0 = rel_subst2(as;r)
26. x: Label
27. (x 1of(unzip(as)))
28. i:
29. i < ||as||
30. < x,apply_alist(as;x;x) > = as[i]
31. xxx: Term
32. 2of(as[i]) = xxx
33. xx: Label
34. 1of(as[i]) = xx
35. s1: smt()
36. f: frame()
37. f A.frame
38. (kind(a) f.acts)
39. s1 = mk_smt(f.var, f.var, f.typ)
40. x'.f.var = s.f.var [[f.typ]] rho
41. t: SimpleType
42. mk_dec(f.var, t) A.ds

t = f.typ

By: AllHyps (i.(Unfold `single_valued_decls` i) THEN (InstHyp [f.var] i) THEN (BackThru -1))

Generated subgoal:

1 11. x:Label, t1,t2:SimpleType. mk_dec(x, t1) A.ds mk_dec(x, t2) A.ds t1 = t2
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. value(a) [[dec_lookup(A.da;kind(a))]] rho
17. 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()
18. 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
19. fr:frame(). fr A.frame (kind(a) fr.acts) x'.fr.var = s.fr.var [[fr.typ]] rho
20. rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr)
21. r@0: rel()
22. as: (LabelTerm) List
23. 1of(unzip(as)) = rel_primed_vars(r)
24. i:. i < ||as|| 2of(as[i]) (x.smts_eff(action_effect(kind(a);A.eff;A.frame);x))(1of(as[i]))
25. r@0 = rel_subst2(as;r)
26. x: Label
27. (x 1of(unzip(as)))
28. i:
29. i < ||as||
30. < x,apply_alist(as;x;x) > = as[i]
31. xxx: Term
32. 2of(as[i]) = xxx
33. xx: Label
34. 1of(as[i]) = xx
35. s1: smt()
36. f: frame()
37. f A.frame
38. (kind(a) f.acts)
39. s1 = mk_smt(f.var, f.var, f.typ)
40. x'.f.var = s.f.var [[f.typ]] rho
41. t: SimpleType
42. mk_dec(f.var, t) A.ds
43. t1,t2:SimpleType. mk_dec(f.var, t1) A.ds mk_dec(f.var, t2) A.ds t1 = t2
mk_dec(f.var, f.typ) A.ds

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