∀ {K : Type u_1} [inst : Field K] {x : K} {R : Subring K} (this : Invertible x)
  (motive : (∃ p, p.leadingCoeff - 1 ∈ ⊥ ∧ (Polynomial.aeval ⅟x⁻¹) p = 0) → Prop)
  (x_1 : ∃ p, p.leadingCoeff - 1 ∈ ⊥ ∧ (Polynomial.aeval ⅟x⁻¹) p = 0),
  (∀ (p : Polynomial ↥R) (hp : p.leadingCoeff - 1 ∈ ⊥) (hpx : (Polynomial.aeval ⅟x⁻¹) p = 0), motive ⋯) → motive x_1