theorem
  X c= Y & Z c= V implies X \/ Z c= Y \/ V
proof
  assume
A1: X c= Y;
  assume
A2: Z c= V;
  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 V by A1,A2;
  hence thesis by XBOOLE_0:def 3;
end;
