reserve f, g, h for Function;
reserve x, y, z, u, X for set,
  A for non empty set,
  n for Element of NAT,
  f for Function of X, X;
reserve f for c=-monotone Function of bool X, bool X,
  S for Subset of X;
reserve X, Y for non empty set,
  f for Function of X, Y,
  g for Function of Y, X;
reserve L for Lattice,
  f for Function of the carrier of L, the carrier of L,
  x for Element of L,
  O, O1, O2, O3, O4 for Ordinal,
  T for Sequence;
reserve L for complete Lattice,
  f for monotone UnOp of L,
  a, b for Element of L;

theorem Th36:
  the carrier of FixPoints f = {x where x is Element of L: x
  is_a_fixpoint_of f}
proof
  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;
  hence thesis by Def8;
end;
