∀ (k : Type u_1) (G : Type u_2) [inst : Semiring k] (x : MonoidAlgebra k (Multiplicative G)),
  (fun x => AddMonoidAlgebra.mapDomain (⇑Multiplicative.ofAdd) x)
      ((fun x => MonoidAlgebra.mapDomain (⇑Multiplicative.toAdd) x) x) =
    x