is mentioned by

Thm* A:ioa{i:l}(), I:Fmla, rho:Decl, de:sig(), e:{[[de]] rho}, te:(LabelLabel). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;te;I) guarded_trace(A.da;te;I) tc_pred(I;A.ds; < > ;de) covers_pred(A;I) closed_pred(I) single_valued_decls(A.ds) let M = [[A]] rho de e in (s:M.state, tr:([[A.da]] rho) List. (M -tr- > s) [[VCs(A;I)]] rho A.ds A.da de e s mk_trace_env(tr, te)) (M |= always s,tr.[[I]] rho A.ds < > de e s mk_trace_env(tr, te))	[vc_trace_correctness]
Thm* A:ioa{i:l}(), I:Fmla, rho:Decl, te:(LabelLabel). ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;te;I) (vVCs(A;I).trace_consistent_vc(rho;A.da;te;v))	[trace_consistent_ioa_inv_vc]
Thm* A:ioa{i:l}(), I:Fmla, rho:Decl, de:sig(), e:{[[de]] rho}, te:(LabelLabel). 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]
Thm* A:ioa{i:l}(), I:Fmla, de:sig(). tc_ioa(A;de) tc_pred(I;A.ds; < > ;de) covers_pred(A;I) closed_pred(I) single_valued_decls(A.ds) tc_vcs{i}(VCs(A;I);A.ds;A.da;de)	[tc_ioa_inv_vc]
Thm* A:ioa{i:l}(), I:Fmla. ioa_trans_all{i}(A;I) VCs	[ioa_trans_all_wf]
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]
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]
Thm* A:ioa{i:l}(), Q:Fmla, rho:Decl, R:(LabelLabel), k:Label. ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;R;Q) trace_consistent_pred(rho;A.da;R;wp(A;k;Q))	[trace_consistent_wp]
Thm* A:ioa{i:l}(), Q:Fmla, de:sig(), a:Label. tc_ioa(A;de) single_valued_decls(A.ds) tc_pred(Q;A.ds;dec_lookup(A.da;a);de) tc_pred(wp(A;a;Q);A.ds;dec_lookup(A.da;a);de)	[tc_wp]
Thm* A:ioa{i:l}(), a:Label, P:Fmla. wp2(A;a;(P)') = wp(A;a;P)	[wp2_addprime]
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]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) (pred_mng_2(pred_unprime(p); rho; ds; da; de; e; s; s'; a; tr) [[p]] rho ds da de e s a tr)	[pred_mng2_unprime]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) (pred_mng_2((p)'; rho; ds; da; de; e; s; s'; a; tr) [[p]] rho ds da de e s' a tr)	[pred_mng2_addprime]
Thm* p:Fmla, 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_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da1;de) closed_pred(p) ([[p]] rho ds da1 de e s a1 tr [[p]] rho ds da2 de e s a2 tr)	[closed_pred_mng]
Thm* A:ioa{i:l}(), Q:Fmla, rho:Decl, R:(LabelLabel), k:Label. ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;R;Q) trace_consistent_pred(rho;A.da;R;wp2(A;k;Q))	[trace_consistent_wp2]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) closed_pred(p) pred_mng_2(p; rho; ds; da; de; e; s; s'; ; tr) Prop	[pred_mng_2_wf_closed]
Thm* da:Collection(dec()), P:Fmla, rho:Decl, te:(LabelLabel). trace_consistent_pred(rho;da;te;P) trace_consistent_pred(rho;da;te;(P)')	[trace_consistent_pred_addprime]
Thm* da:Collection(dec()), P:Fmla, rho:Decl, te:(LabelLabel). trace_consistent_pred(rho;da;te;P) trace_consistent_pred(rho;da;te;pred_unprime(P))	[trace_consistent_pred_unprime]
Thm* p1,p2:Fmla, ds1,ds2,daa:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds1]] rho}, a:[[da1]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p1) tc_pred(p1;ds1;da1;de) p1 = p2 ds1 = ds2 da1 = da2 ([[p1]] rho ds1 da1 de e s a tr [[p2]] rho ds2 da2 de e s a tr)	[pred_mng_functionality]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) [[p]] rho ds da de e s a tr Prop	[pred_mng_wf]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) pred_mng_2(p; rho; ds; da; de; e; s; s'; a; tr) Prop	[pred_mng_2_wf]
Thm* A:ioa{i:l}(), I:Fmla, rho:Decl, te:(LabelLabel), a:dec(). ioa_mentions_trace(A) trace_consistent_pred(rho;A.da;te;I) a A.da trace_consistent_pred(rho;A.da;te;smts_eff_pred(action_effect(a.lbl;A.eff;A.frame);I))	[trace_consistent_action_effect]
Thm* p,q:Fmla, rho:Decl, da:Collection(dec()), R:(LabelLabel). trace_consistent_pred(rho;da;R;p q) trace_consistent_pred(rho;da;R;p) & trace_consistent_pred(rho;da;R;q)	[trace_consistent_pred_and]
Thm* p:Fmla, rho:Decl, da:Collection(dec()), R:(LabelLabel). trace_consistent_pred(rho;da;R;p) Prop	[trace_consistent_pred_wf]
Thm* p:Fmla, ss:Collection(smt()). smts_eff_pred(ss;p) Fmla	[smts_eff_pred_wf]
Thm* p1,p2:Fmla, ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(). p2 p1 ds1 ds2 da1 da2 tc_pred(p1;ds1;da1;de) tc_pred(p2;ds2;da2;de)	[tc_pred_monotone]
Thm* P:Fmla, ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc_pred(P;ds;da;de) tc_pred(pred_unprime(P);ds;da;de)	[tc_pred_unprime]
Thm* P:Fmla, ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc_pred(P;ds;da;de) tc_pred((P)';ds;da;de)	[tc_pred_addprime]
Thm* p1,p2:Fmla, ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(). p1 = p2 ds1 = ds2 da1 = da2 (tc_pred(p1;ds1;da1;de) tc_pred(p2;ds2;da2;de))	[tc_pred_functionality]
Thm* p:Fmla, ds:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(). closed_pred(p) tc_pred(p;ds;da1;de) tc_pred(p;ds;da2;de)	[tc_closed_pred]

In prior sections: mb automata 2 mb automata 3

Try larger context: GenAutomata