
theorem Th14:
  for T being non empty TA-structure for t being type of T, A
  being Subset of the adjectives of T holds A c= adjs t iff t in types A
proof
  let T be non empty TA-structure;
  let t be type of T, a be Subset of the adjectives of T;
  hereby
    assume a c= adjs t;
    then for b being adjective of T st b in a holds t in types b by Th13;
    hence t in types a by Def13;
  end;
  assume
A1: t in types a;
  let x be object;
  assume
A2: x in a;
  then reconsider x as adjective of T;
  t in types x by A1,A2,Def13;
  hence thesis by Th13;
end;
