
theorem
  for T be Tree st for t be Element of T holds succ t = { t^<* 0 *>, t^
  <* 1 *> } holds Leaves T = {}
proof
  let T be Tree;
  assume
A1: for t be Element of T holds succ t = { t^<* 0 *>, t^<* 1 *> };
  assume Leaves T <> {};
  then consider x be object such that
A2: x in Leaves T by XBOOLE_0:def 1;
  reconsider t = x as Element of T by A2;
  succ t = { t^<* 0 *>, t^<* 1 *> } by A1;
  hence contradiction by A2,BINTREE1:3;
end;
