simp only [polyRoot, map_sub, map_one, NumberField.RingOfIntegers.map_mk,
  Algebra.smul_def (ζ - 1), ← mul_div_assoc,
  mul_div_cancel_left₀ _
    ((hζ.map_of_injective (algebraMap K L).injective).sub_one_ne_zero hpri.out.one_lt),
  sub_sub_cancel, smul_smul, inv_mul_cancel (pow_ne_zero _ <| hζ.ne_zero p.pos.ne.symm), one_smul]
case a
K : Type u_1
p : ℕ+
hpri : Fact p.Prime
inst✝⁴ : Field K
inst✝³ : NumberField K
inst✝² : IsCyclotomicExtension {p} ℚ K
hp : p ≠ 2
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
u : (𝓞 K)ˣ
hcong : (↑hζ.unit' - 1) ^ ↑p ∣ ↑u - 1
hu : ∀ (v : K), v ^ ↑p ≠ (algebraMap (𝓞 K) K) ↑u
L : Type u_2
inst✝¹ : Field L
inst✝ : Algebra K L
α : L
e : α ^ ↑p = (algebraMap K L) ((algebraMap (𝓞 K) K) ↑u)
i : ℕ
⊢ (fun x => ζ ^ i • x) α = (fun x => ζ ^ i • x) ((ζ ^ i)⁻¹ • (1 - (ζ - 1) • ↑(polyRoot hp hζ u hcong α e i)))
no goals