
theorem Th17:
  for T1,T2 being TA-structure st the TA-structure of T1 = the
  TA-structure of T2 holds T1 is adjs-typed implies T2 is adjs-typed
proof
  let T1,T2 be TA-structure such that
A1: the TA-structure of T1 = the TA-structure of T2 and
A2: for a being adjective of T1 holds types a \/ types non-a is non empty;
  let b be adjective of T2;
  reconsider a = b as adjective of T1 by A1;
A3: types a \/ types non-a is non empty by A2;
  types a = types b by A1,Th11;
  hence thesis by A1,A3,Th11;
end;
