theorem
  X (+) Y = (X (+) Y) (O) Y & X (-) Y = (X (-) Y) (o) Y
proof
  (X (+) Y) (O) Y =(X (o) Y) (+) Y;
  hence X (+) Y = (X (+) Y) (O) Y by Th50;
  (X (-) Y) (o) Y =(X (O) Y) (-) Y;
  hence thesis by Th50;
end;
