is mentioned by

Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) (pred_mng_2(pred_unprime(p); rho; ds; da; de; e; s; s'; a; tr) [[p]] rho ds da de e s a tr)	[pred_mng2_unprime]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) (pred_mng_2((p)'; rho; ds; da; de; e; s; s'; a; tr) [[p]] rho ds da de e s' a tr)	[pred_mng2_addprime]
Thm* p1,p2:Fmla, ds1,ds2,daa:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds1]] rho}, a:[[da1]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p1) tc_pred(p1;ds1;da1;de) p1 = p2 ds1 = ds2 da1 = da2 ([[p1]] rho ds1 da1 de e s a tr [[p2]] rho ds2 da2 de e s a tr)	[pred_mng_functionality]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) [[p]] rho ds da de e s a tr Prop	[pred_mng_wf]
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) pred_mng_2(p; rho; ds; da; de; e; s; s'; a; tr) Prop	[pred_mng_2_wf]
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* 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,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 vc_mng(v;rho;ds;da;de;e;s;tr) == Case(v) Case vc_imp(hc) = > [[hc.hyp]] rho ds < > de e s mk_trace_env(nil, tr.proj) [[hc.concl]] rho ds < > de e s mk_trace_env(nil, tr.proj) Case vc_qimp(qhc) = > v:[[dec_lookup(da;qhc.lbl)]] rho. [[qhc.hyp]] rho ds dec_lookup(da;qhc.lbl) de e s v tr [[qhc.concl]] rho ds dec_lookup(da;qhc.lbl) de e s v tappend(tr; < qhc.lbl,v > ) Default = > False	[vc_mng]

In prior sections: mb automata 2 mb automata 3

Try larger context: GenAutomata