∀ {k : Type u_1} {G : Type u_2} [inst : AddCommMonoid k] {G' : Type u_3} (f : G → G') (x x_1 : SkewMonoidAlgebra k G),
  ((x + x_1).sum fun a => SkewMonoidAlgebra.single (f a)) =
    (x.sum fun a => SkewMonoidAlgebra.single (f a)) + x_1.sum fun a => SkewMonoidAlgebra.single (f a)