∀ {ι : Type u_1} {R' : Type u_2} {R : Type u_3} {A : ι → Type u_4} [inst : CommSemiring R'] [inst_1 : CommSemiring R]
  [inst_2 : (i : ι) → Semiring (A i)] [inst_3 : Algebra R' R] [inst_4 : (i : ι) → Algebra R (A i)]
  [inst_5 : (i : ι) → Algebra R' (A i)] [∀ (i : ι), IsScalarTower R' R (A i)] (r : R') (i : ι) [inst_7 : DecidableEq ι],
  (algebraMap R' (PiTensorProduct R fun i => A i)) r =
    (PiTensorProduct.tprod R) (Pi.mulSingle i ((algebraMap R' (A i)) r))