theorem Th39:
  for x, y being Element of FixPoints f, a, b st x = a & y = b
  holds (x [= y iff a [= b)
proof
A1: ex P being non empty with_suprema with_infima Subset of L st P = {x where
  x is Element of L: x is_a_fixpoint_of f} & FixPoints f = latt P by Def9;
  let x, y be Element of FixPoints f, a, b;
  assume
A2: x = a & y = b;
  ex a9, b9 being Element of L st x = a9 & y = b9 &( x [= y iff a9 [= b9)
  by A1,Def8;
  hence thesis by A2;
end;
