∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {R' : Type u_3}
  [inst_3 : Semiring R'] [inst_4 : MulSemiringAction R' A] [inst_5 : SMulCommClass R' R A] (_a₁ _a₂ : R')
  (S : Subalgebra R A), Subalgebra.map (MulSemiringAction.toAlgHom R A (_a₁ * _a₂)) S = _a₁ • _a₂ • S