∀ {k : Type u_1} [inst : Field k] {R : Type u_2} [inst_1 : Semiring R] (f : R →+* k) (p : Polynomial R)
  (motive : (∃ x, (Polynomial.map f p).IsRoot x) → Prop) (x : ∃ x, (Polynomial.map f p).IsRoot x),
  (∀ (x : k) (hx : (Polynomial.map f p).IsRoot x), motive ⋯) → motive x