is mentioned by

Thm* A:ioa{i:l}(), r:rel(), rho:Decl, de:sig(), e:{[[de]] rho}, a:([[A.da]] rho), tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_rel(rho;A.da;tr.proj;r) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc(r;A.ds; < > ;de) closed_rel(r) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') ([[r]] rho A.ds < > de e x' tr [[wp_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))	[wp_rel_correctness]
Thm* A:ioa{i:l}(), r:rel(), rho:Decl, de:sig(), e:{[[de]] rho}, a:([[A.da]] rho), tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_rel(rho;A.da;tr.proj;r) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc(r;A.ds; < > ;de) closed_rel(r) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') (rel_mng_2(r; rho; A.ds; < > ; de; e; s; x'; ; tr) [[wp2_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))	[wp2_rel_correctness]
Thm* A:ioa{i:l}(), r:rel(), rho:Decl, de:sig(), e:{[[de]] rho}, a:([[A.da]] rho), tr:trace_env([[A.da]] rho). tc_ioa(A;de) ioa_mentions_trace(A) trace_consistent_rel(rho;A.da;tr.proj;r) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc(r;A.ds;dec_lookup(A.da;kind(a));de) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') (rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr) [[wp2_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr))	[wp2_rel_correct]
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]
Thm* r:rel(), ds1,ds2,da:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds1]] rho}, a:[[da1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds1;da1;de) ds1 = ds2 da1 = da2 ([[r]] rho ds1 da1 de e s a tr [[r]] rho ds2 da2 de e s a tr)	[rel_mng_functionality]
Thm* p:Collection(rel()), ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc_pred(p;ds;da;de) (rp.tc(r;ds;da;de))	[tc_pred_col_all]
Thm* r:rel(), 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_rel(rho;daa;tr.proj;r) tc(r;ds;da1;de) closed_rel(r) ([[r]] rho ds da1 de e s a1 tr [[r]] rho ds da2 de e s a2 tr)	[closed_rel_mng_2]
Thm* rho:Decl, ds,daa:Collection(dec()), da1:Collection(SimpleType), de:sig(), s:{[[ds]] rho}, e:{[[de]] rho}, tr:trace_env([[daa]] rho), r:rel(). closed_rel(r) tc(r;ds;da1;de) trace_consistent_rel(rho;daa;tr.proj;r) [[r]] rho ds da1 de e s tr Prop	[rel_mng_wf_closed]
Thm* r1,r2:rel(), ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s1,s2:{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r1) trace_consistent_rel(rho;daa;tr.proj;r2) tc(r1;ds;da;de) tc(r2;ds;da;de) r1.name = r2.name ||r1.args|| = ||r2.args|| (i:. i < ||r1.args|| [[r1.args[i]]] 1of(e) s1 a tr = [[r2.args[i]]] 1of(e) s1 s2 a tr [[rel_arg_typ(r1.name;i;de)]] rho) ([[r1]] rho ds da de e s1 a tr rel_mng_2(r2; rho; ds; da; de; e; s1; s2; a; tr))	[rel_mng_2_iff]
Thm* r:rel(), ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc_pred( < r > ;ds;da;de) tc(r;ds;da;de)	[tc_pred_singleton]
Thm* r:rel(), ds:Collection(dec()), da:Collection(SimpleType), de:sig(). tc_pred(r;ds;da;de) tc(r;ds;da;de)	[tc_pred_pred_rel]
Thm* r:rel(), ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType), e:{[[de]] rho}, s:{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) [[r]] rho ds st1 de e s a tr Prop	[rel_mng_wf]
Thm* r:rel(), ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType), e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) rel_mng_2(r; rho; ds; st1; de; e; s; s'; a; tr) Prop	[rel_mng_2_wf]
Thm* r:rel(), i:, ds,da:Collection(dec()), st1:Collection(SimpleType), de:sig(), rho:Decl, s:{[[ds]] rho}, e:{1of([[de]] rho)}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) i < ||r.args|| [[r.args[i]]] e s a tr [[rel_arg_typ(r.name;i;de)]] rho	[rel_arg_typing]
Thm* r:rel(), i:, ds,da:Collection(dec()), st1:Collection(SimpleType), de:sig(), rho:Decl, s,s':{[[ds]] rho}, e:{1of([[de]] rho)}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) i < ||r.args|| [[r.args[i]]] e s s' a tr [[rel_arg_typ(r.name;i;de)]] rho	[rel_arg_typing2]
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 tc_pred(P;ds;da;de) == r:rel(). r P tc(r;ds;da;de)	[tc_pred]

In prior sections: mb automata 3

Try larger context: GenAutomata