
theorem Th39:
  for k being Element of NAT, a, b being Element of SubstPoset (
  NAT, {k}) st a <= b & b = {} holds a = {}
proof
  let k be Element of NAT, a, b be Element of SubstPoset (NAT, {k});
  assume
A1: a <= b & b = {};
  Bottom SubstPoset (NAT, {k}) = {} by Th37;
  hence thesis by A1,YELLOW_5:19;
end;
