theorem Th38:
  a in the carrier of FixPoints f iff a is_a_fixpoint_of f
proof
A1: the carrier of FixPoints f = {x where x is Element of L: x
  is_a_fixpoint_of f} by Th36;
  hereby
    assume a in the carrier of FixPoints f;
    then ex b st a = b & b is_a_fixpoint_of f by A1;
    hence a is_a_fixpoint_of f;
  end;
  assume a is_a_fixpoint_of f;
  hence thesis by A1;
end;
