∀ {R : Type u_1} [inst : CommRing R] (m₁ m₂ n : Fin 3 → R),
  ![(m₁ + m₂) 1 * n 2 - (m₁ + m₂) 2 * n 1, (m₁ + m₂) 2 * n 0 - (m₁ + m₂) 0 * n 2,
      (m₁ + m₂) 0 * n 1 - (m₁ + m₂) 1 * n 0] =
    ![m₁ 1 * n 2 - m₁ 2 * n 1, m₁ 2 * n 0 - m₁ 0 * n 2, m₁ 0 * n 1 - m₁ 1 * n 0] +
      ![m₂ 1 * n 2 - m₂ 2 * n 1, m₂ 2 * n 0 - m₂ 0 * n 2, m₂ 0 * n 1 - m₂ 1 * n 0]