∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} (x : Ideal R) (motive : x ∈ {J | I ≤ J ∧ J.IsMaximal} → Prop)
  (x_1 : x ∈ {J | I ≤ J ∧ J.IsMaximal}), (∀ (him : I ≤ x) (hm : x.IsMaximal), motive ⋯) → motive x_1