reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;

theorem
  for f being Function of X,X holds iter(f,0) = id X
proof
  let f be Function of X,X;
  iter(f,0) = id(field f) & field f = dom f by Lm1,Th67,XBOOLE_1:12;
  hence thesis by FUNCT_2:52;
end;
