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* 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* 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:rel(). col_subst(c;r) Collection(rel())	[col_subst_wf_2]
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* 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* r:rel(), as:(LabelTerm) List. (x:Label. unprime(apply_alist(as;x;x)) = x) rel_unprime(rel_subst(as;r)) = rel_unprime(r)	[trivial_rel_subst]
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:Term, as:(LabelTerm) List. (x:Label. unprime(apply_alist(as;x;x)) = x) unprime(term_subst(as;t)) = unprime(t)	[trivial_term_subst]
Thm* t:Term, ds,da,de:Top. term_types(ds;da;de;unprime(t)) ~ term_types(ds;da;de;t)	[term_types_unprime]
Thm* t:Term, ds,da,de:Top. term_types(ds;da;de;(t)') ~ term_types(ds;da;de;t)	[term_types_addprime]
Thm* as:(LabelTerm) List, g:Label, t:Term. subst_mentions_trace(as) term_mentions_guard(g;term_subst2(as;t)) term_mentions_guard(g;t)	[term_subst2_mentions_guard]
Thm* as:(LabelTerm) List, g:Label, t:Term. subst_mentions_trace(as) term_mentions_guard(g;term_subst(as;t)) term_mentions_guard(g;t)	[term_subst_mentions_guard]
Thm* as:(LabelTerm) List. subst_mentions_trace(as) (i:||as||. mentions_trace(2of(as[i])))	[assert_subst_mentions_trace]
Def col_subst2(c;r) == col_map_subst(as.rel_subst2(as;r); < zip(rel_primed_vars(r);s) | s col_list_prod(map(c;rel_primed_vars(r))) > )	[col_subst2]
Def col_subst(c;r) == col_map_subst(as.rel_subst(as;r); < zip(rel_vars(r);s) | s col_list_prod(map(c;rel_vars(r))) > )	[col_subst]

In prior sections: mb automata 1 mb automata 2

Try larger context: GenAutomata