have hpl' : IsPrimitiveRoot (⟨x, hx⟩ : R) l := by
  have nezero : NeZero (l : 𝓞 K) := by
    refine' ⟨fun hzero => _⟩
    simp only [Nat.cast_eq_zero] at hzero
    simp [hzero] at hl
  rw [isRoot_cyclotomic_iff.symm]
  apply hhl
p : ℕ+
K : Type u_1
inst✝² : Field K
ζ✝ : K
hζ✝ : IsPrimitiveRoot ζ✝ ↑p
inst✝¹ : NumberField K
inst✝ : IsCyclotomicExtension {p} ℚ K
x : K
n l : ℕ
hl : l ∈ n.divisors
hx : IsIntegral ℤ x
hhl : (cyclotomic l (𝓞 K)).IsRoot ⟨x, hx⟩
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
h : ¬l ∣ 2 * ↑p
⊢ False
p : ℕ+
K : Type u_1
inst✝² : Field K
ζ✝ : K
hζ✝ : IsPrimitiveRoot ζ✝ ↑p
inst✝¹ : NumberField K
inst✝ : IsCyclotomicExtension {p} ℚ K
x : K
n l : ℕ
hl : l ∈ n.divisors
hx : IsIntegral ℤ x
hhl : (cyclotomic l (𝓞 K)).IsRoot ⟨x, hx⟩
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
h : ¬l ∣ 2 * ↑p
hpl' : IsPrimitiveRoot ⟨x, hx⟩ l
⊢ False