An intuitionistic version of Zermelo's proof that every choice set can be well-ordered

We give a proof, valid in any elementary topos, of the theorem of Zermelo t hat any set possessing a choice function for its set of inhabited subsets c an be well-ordered. Our proof is considerably simpler than existing proofs in the literature and moreover can be seen as a direct generalization of Ze rmelo's own 1908 proof of his theorem.