
theorem Th78:
  for T being adj-structured with_suprema antisymmetric
commutative non empty non void reflexive transitive Noetherian TAS-structure
  for t being type of T holds T@--> reduces t, radix t
proof
  let T be adj-structured with_suprema antisymmetric commutative non empty
  non void reflexive transitive Noetherian TAS-structure;
  let t be type of T;
  set R = T@-->;
  R is with_Church-Rosser_property with_UN_property strongly-normalizing
  Relation by Th69,Th77;
  then nf(t, R) is_a_normal_form_of t, R by REWRITE1:54;
  hence thesis;
end;
