∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Add M] (x y : AddMonoidAlgebra R M),
  x * y = Finsupp.sum x fun m₁ r₁ => Finsupp.sum y fun m₂ r₂ => AddMonoidAlgebra.single (m₁ + m₂) (r₁ * r₂)