simpa [Fin.ext_iff] using finEquivZPowers_symm_apply _ (isOfFinOrder_of_finite σ) n
K : Type u_1
L : Type u_2
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : NumberField K
inst✝² : Algebra K L
inst✝¹ : IsGalois K L
inst✝ : FiniteDimensional K L
σ : L ≃ₐ[K] L
hσ : ∀ (x : L ≃ₐ[K] L), x ∈ Subgroup.zpowers σ
η : L
hη : (Algebra.norm K) η = 1
n : ℕ
⊢ ↑((φ σ) ⟨σ ^ n, ⋯⟩) = n % orderOf σ
no goals