∀ {R : Type u_2} {A : Type u_1} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Module R A]
  (h₁ : ∀ (r : R) (x : A), r • 1 * x = r • x) (r : R) (x : A),
  r • x = { toFun := fun r => r • 1, map_one' := ⋯, map_mul' := ⋯, map_zero' := ⋯, map_add' := ⋯ } r * x