∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
  (h : IsAdjoinRoot S f) {T : Type u_1} [inst_3 : CommRing T] (i : R →+* T) (x : T) (hx : Polynomial.eval₂ i x f = 0),
  h.lift i x hx =
    { toFun := fun z => Polynomial.eval₂ i x (h.repr z), map_one' := ⋯, map_mul' := ⋯, map_zero' := ⋯, map_add' := ⋯ }