theorem
  X is constituted-DTrees implies X /\ Y is constituted-DTrees &
  Y /\ X is constituted-DTrees & X \ Y is constituted-DTrees
proof
  assume
A1: for x st x in X holds x is DecoratedTree;
  thus X /\ Y is constituted-DTrees
  proof
    let x;
    assume x in X /\ Y;
    then x in X by XBOOLE_0:def 4;
    hence thesis by A1;
  end;
  hence Y /\ X is constituted-DTrees;
  let x;
  assume x in X \ Y;
  hence thesis by A1;
end;
