| Rank | Theorem | Name |
| 12 | | | Thm*  A:ioa{i:l}(), I:Fmla, rho:Decl, de:sig(), e:{[[de]] rho}, te:(Label  Label ). tc_ioa(A;de)    ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;te;I) tc_pred(I;A.ds; < > ;de) covers_pred(A;I) guarded_trace(A.da;te;I) closed_pred(I) single_valued_decls(A.ds) (s0,x:[[A]] rho de e.state, act:[[A]] rho de e.action, x':[[A]] rho de e.state, tr:( [[A.da]] rho) List. [[A]] rho de e.init(s0) trace_reachable([[A]] rho de e;s0;mk_trace_env(tr, te).trace;x) [[I]] rho A.ds < > de e x  mk_trace_env(tr, te) [[A]] rho de e.trans(x,act,x') (( t:dec(). t  A.da & t.lbl = kind(act)) [[I]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)) [[I]] rho A.ds < > de e x' tappend(mk_trace_env(tr, te);act)) | [vc_trace_correct_action_decl_lemma] |
| cites |
| 0 | | | Thm* v:Top, rho:Decl. v [[ < > ]] rho | [empty_sts_mng] |
| 10 | | | 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))) | [wp_correctness] |
| 3 | | | Thm* r:rel(), rho:Decl, ds,daa:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), s:{[[ds]] rho}, e:{[[de]] rho}, a1,a2:Top, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r) tc(r;ds;da1;de) closed_rel(r) ([[r]] rho ds da1 de e s a1 tr [[r]] rho ds da2 de e s a2 tr) | [closed_rel_mng_2] |
| 2 | | | Thm* r:rel(), ds:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(). closed_rel(r) tc(r;ds;da1;de) tc(r;ds;da2;de) | [tc_closed_rel] |
| 1 | | | Thm* d:Decl, tr:trace_env(d), a:(d), r:rel(), rho,ds,da,de,e,s,v:Top. affects_trace_rel(tr.proj;kind(a);r) ([[r]] rho ds da de e s v tappend(tr;a) ~ [[r]] rho ds da de e s v tr) | [rel_mng_tappend] |
| 1 | | | Thm* r:rel(), e,a,s,ds,da,de,rho,tr:Top. [[r]] rho ds da de e s a tr ~ [[rel_unprime(r)]] rho ds da de e s a tr | [rel_mng_unprime] |
| 3 | | | Thm* A:ioa{i:l}(), rho:Decl, de:sig(), act:([[A.da]] rho), r,r0:rel(). tc_ioa(A;de) r smts_eff_rel(action_effect(kind(act);A.eff;A.frame);r0) rel_eq(rel_unprime(r);rel_unprime(r0)) (t:dec(). t A.da & t.lbl = kind(act)) | [rel_effect_lemma] |
| 11 | | | 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') ([[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)) | [wp_rel_correctness] |