∀ {m n : ℕ} {R : Type u_2} [inst : Ring R] (f : ↥(Polynomial.degreeLT R (m + n))),
  ↑((Polynomial.degreeLT.addLinearEquiv R m n) f).1 = ↑f %ₘ Polynomial.X ^ m ∧
    ↑((Polynomial.degreeLT.addLinearEquiv R m n) f).2 = ↑f /ₘ Polynomial.X ^ m