reserve X for set;
reserve UN for Universe;

theorem Th56:
  for UN being non trivial Universe holds QUATERNION in UN
  proof
    let UN be non trivial Universe;
A1: QUATERNION c= Funcs(4,REAL) \/ COMPLEX by XBOOLE_1:13;
    4 in UN & REAL is Element of UN by Th16,Th53;
    then Funcs(4,REAL) in UN & COMPLEX in UN by Th55,CLASSES2:61;
    then Funcs(4,REAL) \/ COMPLEX in UN by CLASSES2:60;
    hence thesis by A1,Th13;
  end;
