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;

theorem
  (ex n st x is_a_fixpoint_of iter(f,n) & for y st y is_a_fixpoint_of
  iter(f,n) holds x = y) implies x is_a_fixpoint_of f
proof
  given n such that
A1: x is_a_fixpoint_of iter(f, n) and
A2: for y st y is_a_fixpoint_of iter(f,n) holds x = y;
  dom f = X & dom iter(f, n) = X by FUNCT_2:52;
  hence x in dom f by A1;
  thus thesis by A1,A2,Th2;
end;
