| Rank | Theorem | Name |
| 9 | | | 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). 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') (pred_mng_2(Q; rho; A.ds; < > ; de; e; s; x';  ; tr)  [[wp2(A;kind(a);Q)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))) | [wp2_correctness] |
| cites |
| 0 | | | Thm* v:Top, rho:Decl. v  [[ < > ]] rho | [empty_sts_mng] |
| 8 | | | Thm* 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') (rel_mng_2(r; rho; A.ds; < > ; de; e; s; x'; ; tr) [[wp2_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr)) | [wp2_rel_correctness] |
| 3 | | | Thm* r:rel(), as:(Label Term) List, daa:Collection(dec()), rho:Decl, te:(Label  Label ). trace_consistent_rel(rho;daa;te;r) subst_mentions_trace(as) trace_consistent_rel(rho;daa;te;rel_subst2(as;r)) | [trace_consistent_rel_subst2] |
| 0 | | | Thm* A:ioa{i:l}(), as:(LabelTerm) List, k:Label. ioa_mentions_trace(A) (i: . i < ||as|| 2of(as[i]) smts_eff(action_effect(k;A.eff;A.frame);1of(as[i]))) subst_mentions_trace(as) | [effect_subst_mentions_trace] |
| 4 | | | Thm* A:ioa{i:l}(), Q:Fmla, de:sig(), a:Label. tc_ioa(A;de) tc_pred(Q;A.ds;dec_lookup(A.da;a);de) single_valued_decls(A.ds) tc_pred(wp2(A;a;Q);A.ds;dec_lookup(A.da;a);de) | [tc_wp2] |