∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {f : R →+* S} {I : Ideal S} {p : Polynomial R}
  (motive : (∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ Ideal.comap f I) → Prop)
  (x : ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ Ideal.comap f I),
  (∀ (w : ℕ) (hi : p.coeff w ≠ 0) (mem : p.coeff w ∈ Ideal.comap f I), motive ⋯) → motive x