∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {x : R} (f : R →+* R ⧸ I) (x_1 : Ideal (R ⧸ I))
  (motive : x_1.IsPrime ∧ Ideal.map f (Ideal.span {x}) ≤ x_1 → Prop)
  (x_2 : x_1.IsPrime ∧ Ideal.map f (Ideal.span {x}) ≤ x_1),
  (∀ (hr : x_1.IsPrime) (hxr : Ideal.map f (Ideal.span {x}) ≤ x_1), motive ⋯) → motive x_2