∀ {O : Type u_1} [inst : CommRing O] {p : ℕ} [inst_1 : Fact (Nat.Prime p)] [inst_2 : Fact ¬IsUnit ↑p]
  (motive : (∃ n, (PreTilt.coeff n) 0 ≠ 0) → Prop) (x : ∃ n, (PreTilt.coeff n) 0 ≠ 0),
  (∀ (w : ℕ) (hn : (PreTilt.coeff w) 0 ≠ 0), motive ⋯) → motive x