is mentioned by

Thm* rho:Decl, r:rel(), da:Collection(dec()) , R:(LabelLabel). rel_mentions_trace(r) trace_consistent_rel(rho;da;R;r)	[no_mention_implies_consistent_rel]
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* r:rel(), de:sig(), ds1,ds2:Collection(dec()) , da1,da2:Collection(SimpleType). ds1 ds2 da1 da2 tc(r;ds1;da1;de) tc(r;ds2;da2;de)	[tc_monotone]
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(), ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) tc(rel_unprime(r);ds;da;de)	[tc_unprime]
Thm* r:rel(), ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) tc((r)';ds;da;de)	[tc_addprime]
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]
Thm* r:rel(), ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType) , de:sig(). ds1 = ds2 da1 = da2 (tc(r;ds1;da1;de) tc(r;ds2;da2;de))	[tc_functionality]
Thm* da:Collection(dec()), rho:Decl, tr:trace_env([[da]] rho), y1:Label. trace_consistent(rho;da;tr.proj;trace(y1)) tr.y1 [[lbl_pr( < Trace, y1 > )]] rho	[tproj_w_f2]
Thm* r:rel(), ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) Prop	[tc_wf]
Thm* rho:Decl, t:Term, da:Collection(dec()), R:(LabelLabel). trace_consistent(rho;da;R;t) Prop	[trace_consistent_wf]
Thm* rho:Decl, t:Term, da:Collection(dec()) , R:(LabelLabel). mentions_trace(t) trace_consistent(rho;da;R;t)	[no_mention_implies_consistent_term]
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* d1,d2:Collection(dec()), rho:Decl, u:([[d1]] rho). d1 = d2 u ([[d2]] rho)	[sigma_decls_mng_functionality]
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* ds:Collection(dec()), rho:Decl, a:([[ds]] rho). value(a) [[dec_lookup(ds;kind(a))]] rho	[sigma_decls_mng_value]
Thm* da:Collection(dec()), rho:Decl, k:Label, w:[[dec_lookup(da;k)]] rho. < k,w > ([[da]] rho)	[sigma_decls_mng2]
Thm* ds1,ds2:Collection(dec()), rho:Decl, r:{[[ds1]] rho}. ds2 ds1 r {[[ds2]] rho}	[decls_mng_monotone]
Thm* ds1,ds2:Collection(dec()), rho:Decl, r:{[[ds1]] rho}. ds2 ds1 r {[[ds2]] rho}	[decls_mng_record_subtype]
Thm* ds1,ds2:Collection(dec()), rho:Decl, r:([[ds1]] rho). ds1 = ds2 r ([[ds2]] rho)	[decls_mng_functionality_sigma]
Thm* ds1,ds2:Collection(dec()), rho:Decl, r:{[[ds1]] rho}. ds1 = ds2 r {[[ds2]] rho}	[decls_mng_functionality]
Thm* da:Collection(dec()), rho:Decl, tr:trace_env([[da]] rho), y1:Label. tr.y1 {a:([[da]] rho)| tr.proj(y1,kind(a)) } List	[tproj_w_f]
Thm* d1,d2:Collection(dec()), rho:Decl, u:([[d1]] rho). d2 d1 u ([[d2]] rho)	[sigma_decls_mng_monotone]
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* d:dec(), rho:Decl, s:{[[d]] rho}. s {[[ < d > ]] rho}	[decls_mng_singleton]
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]
Thm* t:Term, ds:Collection(dec()), da1,da2:Collection(SimpleType) , de:sig(). closed_term(t) term_types(ds;da1;de;t) = term_types(ds;da2;de;t)	[term_types_closed]
Thm* ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType), de:sig() , t:Term. ds1 ds2 da1 da2 term_types(ds1;da1;de;t) term_types(ds2;da2;de;t)	[term_types_monotone]
Thm* ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType) , de:sig(), t:Term. ds1 = ds2 da1 = da2 term_types(ds1;da1;de;t) = term_types(ds2;da2;de;t)	[term_types_functionality]
Thm* t:ioa{i:l}(). t.da Collection(dec())	[ioa_da_wf]
Thm* t:ioa{i:l}(). t.ds Collection(dec())	[ioa_ds_wf]
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 [[ds]] rho == [[d]] rho for d {d:dec()| d ds }	[decls_mng]
Def ioa{i:l}() == Collection(dec())Collection(dec())Collection(rel())Collection(pre())Collection(eff()) Collection(frame())	[ioa]

In prior sections: mb automata 2

Try larger context: GenAutomata