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;dec_lookup(A.da;kind(a));de) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') (rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr) [[wp2_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))

Auto
THEN
Try (BackThru Thm* ds:Collection(dec()), rho:Decl, a:([[ds]] rho). value(a) [[dec_lookup(ds;kind(a))]] rho)
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)

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;dec_lookup(A.da;kind(a));de) 15. covers_rel(A;r) 16. [[A]] rho de e.trans(s,a,x') 17. rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr) [[wp2_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr
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;dec_lookup(A.da;kind(a));de) 15. covers_rel(A;r) 16. [[A]] rho de e.trans(s,a,x') 17. [[wp2_rel(A;kind(a);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)
3	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. [[A]] rho de e.trans(s,a,x') trace_consistent_pred(rho;A.da;tr.proj;wp2_rel(A;kind(a);r))
4	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. [[A]] rho de e.trans(s,a,x') tc_pred(wp2_rel(A;kind(a);r);A.ds;dec_lookup(A.da;kind(a));de)

About: