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]] rho m;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]] rho m;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* as:(Label Term) List.
subst_mentions_trace(as)  ( i: ||as||. mentions_trace(2of(as[i]))) | [assert_subst_mentions_trace] |
Def trace_consistent_rel(rho;da;R;r)
== i: ||r.args||. trace_consistent(rho;da;R;r.args[i]) | [trace_consistent_rel] |