reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];

theorem
  a\b \/ b = a \/ b
proof
  a`1 \ b`1 \/ b`1 = a`1 \/ b`1 & a`2 \ b`2 \/ b`2 = a`2 \/ b`2 by XBOOLE_1:39;
  hence thesis;
end;
