  We show how to express intuitionistic Zermelo set theory in deduction modulo
(i.e. by replacing its axioms by rewrite rules) in such a way that the
corresponding notion of proof enjoys the normalization property. To do so, we
first rephrase set theory as a theory of pointed graphs (following a paradigm
due to P. Aczel) by interpreting set-theoretic equality as bisimilarity, and
show that in this setting, Zermelo's axioms can be decomposed into
graph-theoretic primitives that can be turned into rewrite rules. We then show
that the theory we obtain in deduction modulo is a conservative extension of (a
minor extension of) Zermelo set theory. Finally, we prove the normalization of
the intuitionistic fragment of the theory.
