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) 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}(), 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]
Thm* as:(LabelTerm) List, A:ioa{i:l}(), de:sig(), x:Label, t:SimpleType, k:Label. single_valued_decls(A.ds) tc_ioa(A;de) (i:. i < ||as|| 2of(as[i]) smts_eff(action_effect(k;A.eff;A.frame);1of(as[i]))) mk_dec(x, t) A.ds t term_types(A.ds;dec_lookup(A.da;k);de;apply_alist(as;x;x))	[tc_ioa_lemma]
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* r:rel(), as:(LabelTerm) List, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, k:Label, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r) tc(r;ds;da;de) subst_mentions_trace(as) (x:Label. (x rel_primed_vars(r)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)) & s'.x = [[apply_alist(as;x;x)]] 1of(e) s a tr [[t]] rho)) tc(rel_subst2(as;r);ds;da;de) & trace_consistent_rel(rho;daa;tr.proj;rel_subst2(as;r)) & ([[rel_subst2(as;r)]] rho ds da de e s a tr rel_mng_2(r; rho; ds; da; de; e; s; s'; a; tr))	[rel_subst_mng_2_iff]
Def tc_vcs{i}(vs;ds;da;de) == v:vc{i:l}(). v vs tc_vc(v;ds;da;de)	[tc_vcs]
Def [[vs]] rho ds da de e s tr == v:vc{i:l}(). v vs vc_mng(v;rho;ds;da;de;e;s;tr)	[vcs_mng]
Def tc_ioa(A;de) == tc_pred(A.init;A.ds; < > ;de) & (p:pre(). p A.pre tc(p.rel;A.ds;dec_lookup(A.da;p.kind);de)) & (ef:eff(). ef A.eff mk_dec(ef.kind, ef.typ) A.da & tc_eff(ef;A.ds;de)) & (f:frame(). f A.frame mk_dec(f.var, f.typ) A.ds)	[tc_ioa]
Def [[A]] rho de e == mk_sm([[A.da]] rho, [[A.ds]] rho, s.[[A.init]] rho A.ds < > de e s niltrace(), s1,a,s2. (p:pre(). p A.pre p.kind = kind(a) [[p.rel]] rho A.ds dec_lookup(A.da;kind(a)) de e s1 value(a) niltrace()) & (ef:eff(). ef A.eff ef.kind = kind(a) s2.ef.smt.lbl = [[ef.smt.term]] 1of(e) s1 value(a) niltrace() [[ef.smt.typ]] rho) & (fr:frame(). fr A.frame (kind(a) fr.acts) s2.fr.var = s1.fr.var [[fr.typ]] rho))	[ioa_mng]
Def tc_pred(P;ds;da;de) == r:rel(). r P tc(r;ds;da;de)	[tc_pred]

In prior sections: mb collection mb automata 2 mb automata 3

Try larger context: GenAutomata