ZF: Zermelo-Fraenkel Set Theory

This directory contains the ML sources of the Isabelle system for ZF Set Theory, based on FOL.

There are several subdirectories of examples:

AC
subdirectory containing proofs from the book "Equivalents of the Axiom of Choice, II" by H. Rubin and J.E. Rubin, 1985. Thanks to Krzysztof Gr`abczewski.

Coind
subdirectory containing a large example of proof by co-induction. It is by Jacob Frost following a paper by Robin Milner and Mads Tofte.

IMP
subdirectory containing a semantics equivalence proof between operational and denotational definitions of a simple programming language. Thanks to Heiko Loetzbeyer & Robert Sandner.

Resid
subdirectory containing a proof of the Church-Rosser Theorem. It is by Ole Rasmussen, following the Coq proof by G´┐Żard Huet.

ex
subdirectory containing various examples.
Isabelle/ZF formalizes the greater part of elementary set theory, including relations, functions, injections, surjections, ordinals and cardinals. Results proved include Cantor's Theorem, the Recursion Theorem, the Schroeder-Bernstein Theorem, and (assuming AC) the Wellordering Theorem.

Isabelle/ZF also provides theories of lists, trees, etc., for formalizing computational notions. It supports inductive definitions of infinite-branching trees for any cardinality of branching.

Useful references for Isabelle/ZF:

Useful references on ZF set theory: