
theorem
  for T being Noetherian adj-structured reflexive transitive
  antisymmetric with_suprema TA-structure for t being type of T for A being
Subset of the adjectives of T st A c= adjs t holds A is_applicable_to t & A ast
  t = t
proof
  let T be Noetherian adj-structured reflexive transitive antisymmetric
  with_suprema TA-structure;
  let t be type of T;
  let a be Subset of the adjectives of T;
  assume
A1: a c= adjs t;
  hence a is_applicable_to t by Th52;
  then
A2: a ast t <= t by Th49;
  t <= a ast t by A1,Th52;
  hence thesis by A2,YELLOW_0:def 3;
end;
