
theorem Th75:
  for x,y,z being set st z in x U+ y holds z = [z`1,z`2] & (z`2 =
  1 & z`1 in x or z`2 = 2 & z`1 in y)
proof
  let x,y,z be set;
  assume z in x U+ y;
  then z in [:x,{1}:] \/ [:y,{2}:] by Th73;
  then z in [:x,{1}:] or z in [:y,{2}:] by XBOOLE_0:def 3;
  hence thesis by MCART_1:13,21;
end;
