  Automated Market Makers (AMMs) are an integral component of the decentralized
finance (DeFi) ecosystem, as they allow users to exchange crypto-assets without
the need for trusted authorities or external price oracles. Although these
protocols are based on relatively simple mechanisms, e.g., to algorithmically
determine the exchange rate between crypto-assets, they give rise to complex
economic behaviours. This complexity is witnessed by the proliferation of
models that study their structural and economic properties. Currently, most of
theoretical results obtained on these models are supported by pen-and-paper
proofs. This work proposes a formalization of constant-product AMMs in the Lean
4 Theorem Prover. To demonstrate the utility of our model, we provide
mechanized proofs of key economic properties like arbitrage, that at the best
of our knowledge have only been proved by pen-and-paper before.
