∀ (num num_1 : ℤ) (e_num : num = num_1) (den den_1 : ℕ) (e_den : den = den_1) (g g_1 : ℕ) (e_g : g = g_1)
  (dvd_num : ↑g ∣ num) (dvd_den : g ∣ den) (den_nz : den / g ≠ 0) (reduced : (num / ↑g).natAbs.Coprime (den / g)),
  Rat.maybeNormalize num den g dvd_num dvd_den den_nz reduced = Rat.maybeNormalize num_1 den_1 g_1 ⋯ ⋯ ⋯ ⋯