We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.
 A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs, and other computational reasoning. A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higher-order syntax supports the definition of new binding operators. Unknowns in subgoals can be instantiated incrementally. The paper describes the derivation of rules for descriptions, relations, and functions and discusses interactive proofs of Cantor's Theorem, the Composition of Homomorphisms challenge [9], and Ramsey's Theorem [5]. A generic proof assistant can stand up against provers dedicated to particular logics.