∀ {ι : Type u_1} (A : ι → Type u_2) [inst : (i : ι) → Semiring (A i)] (S : ι → Type u_3)
  [inst_1 : (i : ι) → CommSemiring (S i)] [inst_2 : (i : ι) → Algebra (S i) (A i)] (x : (i : ι) → S i)
  (x_1 : (i : ι) → A i), x • x_1 = (Pi.ringHom fun x => (algebraMap (S x) (A x)).comp (Pi.evalRingHom S x)) x * x_1