reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X c= Y implies X \/ Z c= Y \/ Z
proof
  assume
A1: X c= Y;
  let x be object;
  assume x in X \/ Z;
  then x in X or x in Z by XBOOLE_0:def 3;
  then x in Y or x in Z by A1;
  hence thesis by XBOOLE_0:def 3;
end;
