An encoding of Zermelo-Fraenkel Set Theory in Coq. The encoding of Zermelo-Fraenkel Set Theory is largely inspired by Peter Aczel's work dating back to the eighties. A type Ens is defined, which represents sets. Two predicates IN and EQ stand for membership and extensional equality between sets. The axioms of ZFC are then proved and thus appear as theorems in the development. A main motivation for this work is the comparison of the respective expressive power of Coq and ZFC. A non-computational type-theoretical axiom of choice is necessary to prove the replacement schemata and the set-theoretical AC. The main difference between this work and Peter Aczel's is that propositions are defined on the impredicative level Prop. Since the definition of Ens is, however, still unchanged, I also added most of Peter Aczel's definition. The main advantage of Aczel's approach is a more constructive vision of the existential quantifier (which gives the set-theoretical axiom of choice for free).
opam install coq-zfc.8.7.0