reserve x, y, z, E, E1, E2, E3 for set,
  sE for Subset-Family of E,
  f for Function of E, E,
  k, l, m, n for Nat;

theorem Th3:
  for E being non empty set, f being Function of E, E, x being
  Element of E holds iter(f,0).x = x
proof
  let E be non empty set, f be Function of E, E, x be Element of E;
  dom f = E by FUNCT_2:def 1;
  then
A1: x in dom f \/ rng f by XBOOLE_0:def 3;
  thus iter(f,0).x = id(field f).x by FUNCT_7:68
    .= x by A1,FUNCT_1:17;
end;
