Authors: Riccardo Brasca ^1,2; Christopher Birkbeck ³; Eric Rodriguez Boidi ; Alex Best ; Ruben van De Velde ; Andrew Yang ⁴

• 1 Institut de Mathématiques de Jussieu - Paris Rive Gauche [UPCité]
• 2 Université Paris Cité [UPCité]
• 3 University of East Anglia [Norwich] [UEA]
• 4 Imperial College London

We formalize a complete proof of the regular case of Fermat's Last Theorem in the Lean4 theorem prover. Our formalization includes a proof of Kummer's lemma, that is the main obstruction to Fermat's Last Theorem for regular primes. Rather than following the modern proof of Kummer's lemma via class field theory, we prove it by using Hilbert's Theorems 90-94 in a way that is more amenable to formalization.