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

Unfolds [`tc`;`rel_arg_typ`] 0
THEN
Analyze 0
THEN
Analyze 1
THEN
Analyze 1
THEN
Reduce 0
THEN
Try ((Fold `mk_rel` 0) THEN (Folds [`relname_other`;`relname_eq`] 0))
THEN
ExRepD
THEN
Using [`de',de] (BackThru 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)
THEN
SmAuto
THEN
AllHyps (h.(Unfold `trace_consistent_rel` h) THEN (Reduce h) THEN (InstHyp [i] h) THEN (Complete Auto))

1

1. x: SimpleType 2. r1: Term List 3. i: 4. ds: Collection(dec()) 5. da: Collection(dec()) 6. st1: Collection(SimpleType) 7. de: sig() 8. rho: Decl 9. s: {[[ds]] rho} 10. e: {1of([[de]] rho)} 11. a: [[st1]] rho 12. tr: trace_env([[da]] rho) 13. trace_consistent_rel(rho;da;tr.proj; < inl(x),r1 > ) 14. ||r1|| = 2 15. x term_types(ds;st1;de;r1[0]) 16. x term_types(ds;st1;de;r1[1]) 17. i < ||r1|| x term_types(ds;st1;de;r1[i])

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