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, 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}(), 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* 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* 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* 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 3

Try larger context: GenAutomata