
theorem
  for T be binary Tree for n be Nat for t be Element of T st
  t in T-level n holds t is Element of n-tuples_on BOOLEAN
proof
  let T be binary Tree;
  let n be Nat;
  let t be Element of T;
  assume t in T-level n;
  then t in { w where w is Element of T : len w = n } by TREES_2:def 6;
  then ex t2 be Element of T st t2 = t & len t2 = n;
  hence thesis by FINSEQ_2:92;
end;
