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* 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* 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* d:Decl, tr:trace_env(d), a:( d), r:rel(), rho,ds,da,de,e,s,v:Top.
affects_trace_rel(tr.proj;kind(a);r) 
([[r]] rho ds da de e s v tappend(tr;a) ~ [[r]] rho ds da de e s v tr) | [rel_mng_tappend] |
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] |