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