AC -- Equivalents of the Axiom of Choice

Krzysztof Grabczewski has mechanized the first two chapters of the book

@book{rubin&rubin,
  author	= "Herman Rubin and Jean E. Rubin",
  title		= "Equivalents of the Axiom of Choice, {II}",
  publisher	= "North-Holland",
  year		= 1985}

The report Mechanizing Set Theory, by Paulson and Grabczewski, describes both this development and ZF's theories of cardinals.