∀ {R : Type u_1} [inst : CommSemiring R] {s : Set (PrimeSpectrum R)}
  (motive : (∃ s_1, s_1.Finite ∧ s = (PrimeSpectrum.zeroLocus s_1)ᶜ) → Prop)
  (x : ∃ s_1, s_1.Finite ∧ s = (PrimeSpectrum.zeroLocus s_1)ᶜ),
  (∀ (s_1 : Set R) (hs : s_1.Finite) (e : s = (PrimeSpectrum.zeroLocus s_1)ᶜ), motive ⋯) → motive x