reserve x,y,z for object, X,Y for set,
  i,k,n for Nat,
  p,q,r,s for FinSequence,
  w for FinSequence of NAT,
  f for Function;

theorem
  X is constituted-Trees & Y is constituted-Trees implies
  X \+\ Y is constituted-Trees
proof
  assume that
A1: for x st x in X holds x is Tree and
A2: for x st x in Y holds x is Tree;
  let x;
  assume x in X \+\ Y;
  then not x in X iff x in Y by XBOOLE_0:1;
  hence thesis by A1,A2;
end;
