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
  iter(id(X),n) = id(X)
proof
  defpred P[Nat] means iter(id(X),$1) = id(X);
A1: P[k] implies P[k+1]
  proof
    assume
A2: P[k];
    thus iter(id(X),k+1) = iter(id(X),k)*id(X) by Th68
      .= id(X) by A2,FUNCT_2:17;
  end;
  id(field id X) = id X;
  then
A3: P[ 0] by Th67;
  P[k] from NAT_1:sch 2(A3,A1);
  hence thesis;
end;
