
theorem Th8:
  for N being non empty Poset holds IdsMap N is one-to-one
proof
  let N be non empty Poset;
  set f = IdsMap N;
  let x, y be Element of N such that
A1: f.x = f.y;
  f.x = downarrow x & f.y = downarrow y by YELLOW_2:def 4;
  hence thesis by A1,WAYBEL_0:19;
end;
