∀ {R : Type u_3} {B : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B]
  (fg :
    { fg //
      (∀ (x y : A), fg.2 x * fg.2 y = 0) ∧
        (∀ (r x : A), fg.2 (r • x) = fg.1 r * fg.2 x) ∧ ∀ (r x : A), fg.2 (MulOpposite.op r • x) = fg.2 x * fg.1 r })
  (x : A), (↑fg).1 x * (↑fg).2 1 = (↑fg).2 x