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

theorem Th12:
  X c= Y implies X \/ Y = Y
proof
  assume
A1: X c= Y;
  thus X \/ Y c= Y
  proof
    let x be object;
    assume x in X \/ Y;
    then x in X or x in Y by XBOOLE_0:def 3;
    hence thesis by A1;
  end;
  let x be object;
  thus thesis by XBOOLE_0:def 3;
end;
