
theorem Th6:
  for f being Function, x being set st x in dom f holds x in f orbit x
proof
  let f be Function;
  let x be set;
  assume x in dom f;
  then
A1: x in dom f \/ rng f by XBOOLE_0:def 3;
A2: iter(f,0) = id (field f) by FUNCT_7:68;
  then
A3: iter(f,0).x = x by A1,FUNCT_1:17;
  dom iter(f,0) = dom f \/ rng f by A2;
  hence thesis by A1,A3;
end;
