∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] [inst_2 : DecidableEq α] (f : Associates α →* α)
  (hinv : Function.RightInverse (⇑f) Associates.mk) (u : αˣ), (if ↑u = 0 then 1 else Classical.choose ⋯) = u⁻¹