no goals
𝕜 : Type u
A : Type v
inst✝³ : Field 𝕜
inst✝² : Ring A
inst✝¹ : Algebra 𝕜 A
inst✝ : IsAlgClosed 𝕜
a : A
n : ℕ
hn : 0 < n
⊢ σ (a ^ n) = (fun x => x ^ n) '' σ a
simpa only [aeval_X_pow, eval_pow, eval_X]
  using map_polynomial_aeval_of_degree_pos a (X ^ n : 𝕜[X]) (by rwa [degree_X_pow, Nat.cast_pos])
no goals
𝕜 : Type u
A : Type v
inst✝³ : Field 𝕜
inst✝² : Ring A
inst✝¹ : Algebra 𝕜 A
inst✝ : IsAlgClosed 𝕜
a : A
n : ℕ
hn : 0 < n
⊢ 0 < degree (X ^ n)
rwa [degree_X_pow, Nat.cast_pos]