  The proof of the relative consistency of the axiom of choice has been
mechanized using Isabelle/ZF. The proof builds upon a previous mechanization of
the reflection theorem. The heavy reliance on metatheory in the original proof
makes the formalization unusually long, and not entirely satisfactory: two
parts of the proof do not fit together. It seems impossible to solve these
problems without formalizing the metatheory. However, the present development
follows a standard textbook, Kunen's Set Theory, and could support the
formalization of further material from that book. It also serves as an example
of what to expect when deep mathematics is formalized.
