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

(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.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(). r' col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r)
23. tc(r;A.ds;dec_lookup(A.da;kind(a));de)

r':rel(). r' col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r) & tc(r';A.ds;dec_lookup(A.da;kind(a));de) & trace_consistent_rel(rho;A.da;tr.proj;r') & ([[r']] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr))

By: ExRepD THEN InstConcl [r'] THEN Analyze 0 THEN Try Trivial THEN Try ((Reduce 0) THEN (Complete Auto))

Generated subgoals:

1 22. r': rel()
23. r' col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r)
24. tc(r;A.ds;dec_lookup(A.da;kind(a));de)
tc(r';A.ds;dec_lookup(A.da;kind(a));de) & trace_consistent_rel(rho;A.da;tr.proj;r') & ([[r']] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr))

2 22. r': rel()
23. r' col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r)
24. tc(r;A.ds;dec_lookup(A.da;kind(a));de)
25. r1: rel()
col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r) Collection(rel())

About:

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

1	22. `r':` `rel()` 23. `r' col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r)` 24. `tc(r;A.ds;dec_lookup(A.da;kind(a));de)` `tc(r';A.ds;dec_lookup(A.da;kind(a));de) & trace_consistent_rel(rho;A.da;tr.proj;r') & ([[r']] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr))`
2	22. `r':` `rel()` 23. `r' col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r)` 24. `tc(r;A.ds;dec_lookup(A.da;kind(a));de)` 25. `r1:` `rel()` `col_subst2(x.smts_eff(action_effect(kind(a);A.eff;A.frame);x);r) Collection(rel())`