∀ {M₀ : Type u_1} {N₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : MulZeroOneClass N₀]
  [inst_2 : DecidablePred fun x => x = 0] [inst_3 : Nontrivial M₀] [inst_4 : NoZeroDivisors M₀] (x : M₀ˣ), 1 ↑x = 1