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

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

tc(rel_subst2(as;r);A.ds;dec_lookup(A.da;kind(a));de) & trace_consistent_rel(rho;A.da;tr.proj;rel_subst2(as;r)) & ([[rel_subst2(as;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:
(Inst Thm* r:rel(), as:(LabelTerm) List, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, k:Label, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r) tc(r;ds;da;de) subst_mentions_trace(as) (x:Label. (x rel_primed_vars(r)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)) & s'.x = [[apply_alist(as;x;x)]] 1of(e) s a tr [[t]] rho)) tc(rel_subst2(as;r);ds;da;de) & trace_consistent_rel(rho;daa;tr.proj;rel_subst2(as;r)) & ([[rel_subst2(as;r)]] rho ds da de e s a tr rel_mng_2(r; rho; ds; da; de; e; s; s'; a; tr)) [r;as;A.ds;A.da;dec_lookup(A.da;kind(a));de;rho;e;s;x';kind(a);value(a);tr]) THENA (Try (Complete Auto))
THEN
TrivialIoaHyp
Generated subgoals:

1 subst_mentions_trace(as)
2 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)
328. tc(rel_subst2(as;r);A.ds;dec_lookup(A.da;kind(a));de) & trace_consistent_rel(rho;A.da;tr.proj;rel_subst2(as;r)) & ([[rel_subst2(as;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))
tc(rel_subst2(as;r);A.ds;dec_lookup(A.da;kind(a));de) & trace_consistent_rel(rho;A.da;tr.proj;rel_subst2(as;r)) & ([[rel_subst2(as;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))

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