
theorem Th13:
  for T being TA-structure for t being type of T, a being
  adjective of T holds a in adjs t iff t in types a
proof
  let T be TA-structure;
  let t be type of T, a be adjective of T;
  thus a in adjs t implies t in types a by Def12;
  assume t in types a;
  then ex t9 being type of T st t = t9 & a in adjs t9 by Def12;
  hence thesis;
end;
