A:ioa{i:l}(), r:rel(), rho:Decl, de:sig(), e:{[[de]] rho}, a:([[A.da]] rho), tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_rel(rho;A.da;tr.proj;r) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc(r;A.ds; < > ;de) closed_rel(r) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') ([[r]] rho A.ds < > de e x' tr [[wp_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))

let T Auto THEN TrivialIoaHyp THEN (Try (Reduce 0)) THEN (Try (Unfold `decl` 0)) THEN (Try (BackThru Thm* v:Top, rho:Decl. v [[ < > ]] rho)) THEN (Try ((Unfold `ioa_mng` 0) THEN (Reduce 0) THEN Trivial)) THEN (Try (Unfolds [`pred_rel`;`tc_pred`;`closed_pred`;`trace_consistent_pred`] 0)) THEN (Try (Unfold `col_all` 0)) THEN (Try (RW ColMemberC 0)) THEN SimpConcl in ((RepeatFor 17 ((Analyze 0) THENA (Complete T))) THEN (Inst Thm* A:ioa{i:l}(), de:sig(). tc_ioa(A;de) ioa_mentions_trace(A) (Q:Fmla, rho:Decl, e:{[[de]] rho}, a:[[A]] rho de e.action, tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;tr.proj;Q) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc_pred(Q;A.ds; < > ;de) closed_pred(Q) covers_pred(A;Q) [[A]] rho de e.trans(s,a,x') ([[Q]] rho A.ds < > de e x' tr [[wp(A;kind(a);Q)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))) [A;de;r;rho;e;a;tr;s;x'])) THENA T

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]] rho de e.state 13. x': [[A]] rho de e.state 14. tc(r;A.ds; < > ;de) 15. closed_rel(r) 16. covers_rel(A;r) 17. [[A]] rho de e.trans(s,a,x') covers_pred(A; < r > )

2

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; < > ;de) 15. closed_rel(r) 16. covers_rel(A;r) 17. [[A]] rho de e.trans(s,a,x') 18. [[r]] rho A.ds < > de e x' tr [[wp(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr [[r]] rho A.ds < > de e x' tr [[wp_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr

About: