∀ {R : Type u_2} {ι : Type u_1} [inst : CommSemiring R] {s : Finset ι} {f : ι → Ideal R} (x : ι)
  (motive : x ∈ s ∧ f x ≤ s.inf f → Prop) (x_1 : x ∈ s ∧ f x ≤ s.inf f),
  (∀ (h1 : x ∈ s) (h2 : f x ≤ s.inf f), motive ⋯) → motive x_1