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

Journal of Symbolic Logic 66 (3):1121-1126 (2001)
We give a proof, valid in any elementary topos, of the theorem of Zermelo that any set possessing a choice function for its set of inhabited subsets can be well-ordered. Our proof is considerably simpler than existing proofs in the literature and moreover can be seen as a direct generalization of Zermelo's own 1908 proof of his theorem
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