is mentioned by

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]
Thm* ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType) , e1:{1of([[de]] rho)}, s:{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho), l:Term List. (i:||l||. trace_consistent(rho;da;tr.proj;l[i])) (ls:SimpleType List, f:reduce(s,m. [[s]] rhom;Prop;ls). ||ls|| = ||l|| & (i:. i < ||l|| ls[i] term_types(ds;st1;de;l[i])) list_accum(x,t.x([[t]] e1 s a tr);f;l) Prop)	[rel_mng_lemma]
Thm* ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType) , e1:{1of([[de]] rho)}, s,s':{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho), l:Term List. (i:||l||. trace_consistent(rho;da;tr.proj;l[i])) (ls:SimpleType List, f:reduce(s,m. [[s]] rhom;Prop;ls). ||ls|| = ||l|| & (i:. i < ||l|| ls[i] term_types(ds;st1;de;l[i])) list_accum(x,t.x([[t]] e1 s s' a tr);f;l) Prop)	[rel_mng_2_lemma]
Thm* ds,da:Collection(dec()), st1:Collection(SimpleType), de:sig(), rho:Decl , t:Term, s:{[[ds]] rho}, e:{1of([[de]] rho)}, a:SimpleType, v:[[st1]] rho , tr:trace_env([[da]] rho). trace_consistent(rho;da;tr.proj;t) a term_types(ds;st1;de;t) [[t]] e s v tr [[a]] rho	[term_typing]
Thm* ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl , t:Term, s,s':{[[ds]] rho}, e:{1of([[de]] rho)}, a:SimpleType, v:[[da]] rho , tr:trace_env([[daa]] rho). trace_consistent(rho;daa;tr.proj;t) a term_types(ds;da;de;t) [[t]] e s s' v tr [[a]] rho	[term_typing2]
Thm* ds,da:Collection(dec()), st:Collection(SimpleType), de:sig(), rho:Decl , e1:{1of([[de]] rho)}, s1,s2:{[[ds]] rho}, a:[[st]] rho, tr:trace_env([[da]] rho), u:Term , t:SimpleType. trace_consistent(rho;da;tr.proj;u) (x:Label. (x term_vars(u)) s1.x = s2.x) t term_types(ds;st;de;u) [[u]] e1 s1 a tr = [[u]] e1 s2 a tr [[t]] rho	[term_mng_equal]
Thm* r:rel(), as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) (x:Label. (x rel_vars(r)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) tc(rel_subst(as;r);ds;da;de)	[rel_subst_tc]
Thm* r:rel(), as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) (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)))) tc(rel_subst2(as;r);ds;da;de)	[rel_subst2_tc]
Thm* r:rel(), I:Fmla, A:ioa{i:l}(), a:Label. covers_pred(A;I) r I (r':rel(). r' col_subst2(x.smts_eff(action_effect(a;A.eff;A.frame);x);r))	[covers_pred_lemma2]
Thm* c:(LabelCollection(Term)), r,r':rel(). r' col_subst2(c;r) (as:(LabelTerm) List. 1of(unzip(as)) = rel_primed_vars(r) & (i:. i < ||as|| 2of(as[i]) c(1of(as[i]))) & r' = rel_subst2(as;r))	[member_col_subst2]
Thm* c:(LabelCollection(Term)), r,r':rel(). r' col_subst(c;r) (as:(LabelTerm) List. 1of(unzip(as)) = rel_vars(r) & (i:. i < ||as|| 2of(as[i]) c(1of(as[i]))) & r' = rel_subst(as;r))	[member_col_subst]
Thm* A:ioa{i:l}(), I:Fmla, r:rel(). r I covers_pred(A;I) covers_rel(A;r)	[covers_pred_rel_member]
Thm* ds:Collection(dec()), rho:Decl, a:([[ds]] rho), x:Label. mk_dec(kind(a), x) ds value(a) rho(x)	[sigma_decls_mng_value2]
Thm* ds:Collection(dec()), rho:Decl, s:{[[ds]] rho}, x:Label , t:SimpleType. t dec_lookup(ds;x) s.x [[t]] rho	[record_select_wf_decls_mng2]
Thm* ds:Collection(dec()), rho:Decl, s:{[[ds]] rho}, x:Label , t:SimpleType. mk_dec(x, t) ds s.x [[t]] rho	[record_select_wf_decls_mng]
Thm* ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType) , de:sig(), t:Term. ds1 ds2 da1 da2 (a:SimpleType. a term_types(ds1;da1;de;t) a term_types(ds2;da2;de;t))	[term_types_monotone_member]
Thm* ds1,ds2:Collection(dec()), x,y:Label, rho:Decl , v:[[ds1]] rho(x). (d:dec(). d ds2 d.lbl = y mk_dec(x, d.typ) ds1) v [[ds2]] rho(y)	[decls_mng_rename_member]
Thm* ds:Collection(dec()), rho:Decl, x:Label, y:[[ds]] rho(x) , a:SimpleType. mk_dec(x, a) ds y [[a]] rho	[decls_mng_subtype]
Thm* ds1,ds2:Collection(dec()), x:Label, rho:Decl, v:[[ds1]] rho(x). (d:dec(). d ds2 d.lbl = x d ds1) v [[ds2]] rho(x)	[decls_mng_member]
Thm* t:Term, s:SimpleType, as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). s term_types(ds;da;de;t) (x:Label. (x term_primed_vars(t)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) s term_types(ds;da;de;term_subst2(as;t))	[term_subst2_tc]
Thm* t:Term, s:SimpleType, as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). s term_types(ds;da;de;t) (x:Label. (x term_vars(t)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) s term_types(ds;da;de;term_subst(as;t))	[term_subst_tc]
Def pred_mng_2(p; rho; ds; da; de; e; s; s'; a; tr) == r:rel(). r p rel_mng_2(r; rho; ds; da; de; e; s; s'; a; tr)	[pred_mng_2]
Def ioa_mentions_trace(A) == (e:eff(). e A.eff & mentions_trace(e.smt.term)) (p:pre(). p A.pre & rel_mentions_trace(p.rel)) (r:rel(). r A.init & rel_mentions_trace(r))	[ioa_mentions_trace]
Def closed_pred(p) == r:rel(). r p closed_rel(r)	[closed_pred]
Def [[p]] rho ds da de e s a tr == r:rel(). r p [[r]] rho ds da de e s a tr	[pred_mng]
Def guarded_trace(da;e;I) == r:rel(). r I (k:Label. affects_trace_rel(e;k;r) (t:dec(). t da & t.lbl = k))	[guarded_trace]
Def tc_smt(s;ds;da;de) == mk_dec(s.lbl, s.typ) ds & s.typ term_types(ds;da;de;s.term)	[tc_smt]
Def tc(r;ds;da;de) == Case(r.name) Case eq(Q) = > ||r.args|| = 2 & Q term_types(ds;da;de;r.args[0]) & Q term_types(ds;da;de;r.args[1]) Case R = > ||de.rel(R)|| = ||r.args|| & (i:. i < ||r.args|| (de.rel(R))[i] term_types(ds;da;de;r.args[i])) Default = > False	[tc]
Def [[ds]] rho == [[d]] rho for d {d:dec()| d ds }	[decls_mng]

In prior sections: mb collection mb automata 2

Try larger context: GenAutomata