
theorem Th7:
  for T be Tree st for t be Element of T holds succ t = { t^<* 0 *>
  , t^<* 1 *> } holds T is binary
proof
  let T be Tree;
  assume for t be Element of T holds succ t = { t^<* 0 *>, t^<* 1 *> };
  then
  for t be Element of T st not t in Leaves T holds succ t = { t^<* 0 *>, t
  ^<* 1 *> };
  hence thesis by BINTREE1:def 2;
end;
