We present a formalization of Borel determinacy in the Lean 4 theorem prover. The formalization includes a definition of Gale-Stewart games and a proof of Martin's theorem stating that Borel games are determined. The proof closely follows Martin's "A purely inductive proof of Borel determinacy".

Final version, to appear in Annals of Formalized Mathematics

• 03E60 - Determinacy principles
• 68V20 - Formalization of mathematics in connection with theorem provers