∀ {X : Type u_1} {R : Type u_2} [inst : Zero X] [inst_1 : TopologicalSpace X] [inst_2 : TopologicalSpace R]
  [inst_3 : CommSemiring R] [inst_4 : IsTopologicalSemiring R] [inst_5 : StarRing R] [inst_6 : ContinuousStar R]
  (x x_1 : ContinuousMapZero X R),
  { toContinuousMap := star ↑(x * x_1), map_zero' := ⋯ } =
    { toContinuousMap := star ↑x_1, map_zero' := ⋯ } * { toContinuousMap := star ↑x, map_zero' := ⋯ }