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Elliptic curves are fundamental objects in number theory and algebraicgeometry, whose points over a field form an abelian group under a geometricaddition law. Any elliptic curve over a field admits a Weierstrass model, butprior formal proofs that the addition law is associative in this model involveeither advanced algebraic geometry or tedious computation, especially incharacteristic two. We formalise in the Lean theorem prover, the type ofnonsingular points of a Weierstrass curve over a field of any characteristicand a purely algebraic proof that it forms an abelian group.

An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in any Characteristic