∀ (n : ℕ) (x y : ↥(rootsOfUnity n Circle)),
  (↑((rootsOfUnityUnitsMulEquiv ℂ n).toMonoidHom.comp (restrictRootsOfUnity Circle.toUnits n))).toFun (x * y) =
    (↑((rootsOfUnityUnitsMulEquiv ℂ n).toMonoidHom.comp (restrictRootsOfUnity Circle.toUnits n))).toFun x *
      (↑((rootsOfUnityUnitsMulEquiv ℂ n).toMonoidHom.comp (restrictRootsOfUnity Circle.toUnits n))).toFun y