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
  for T1,T2, W1,W2 being Tree st T1 c= W1 & T2 c= W2 holds
  tree(T1,T2) c= tree(W1,W2)
proof
  let T1,T2, W1,W2 be Tree such that
A1: T1 c= W1 and
A2: T2 c= W2;
  let x be object;
  assume x in tree(T1,T2);
  then reconsider p = x as Element of tree(T1,T2);
  p = {} or ex q st q in T1 & p = <*0*>^q or q in T2 & p = <*1*>^q by Th68;
  hence thesis by A1,A2,Th68;
end;
