theorem extracted_formal_statement_147 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} {b : Fin ↑m → ℝ} {Ane0 : A ≠ 0}
  (x₁ : EuclideanSpace ℝ (Fin ↑n)) :
  HasGradientAt (fun x => 1 / 2 * ‖A *ᵥ x - b‖ ^ 2) ((fun x => Aᵀ *ᵥ (A *ᵥ x - b)) x₁) x₁ := sorry

State before:
n m : ℕ+
A : Matrix (Fin ↑m) (Fin ↑n) ℝ
b : Fin ↑m → ℝ
μ : ℝ
μpos : 0 < μ
Ane0 : A ≠ 0
x₀ : EuclideanSpace ℝ (Fin ↑n)
p : LASSO A b μ μpos Ane0 x₀
⊢ ∀ (x₁ : EuclideanSpace ℝ (Fin ↑n)),
    HasGradientAt (fun x => 1 / 2 * ‖A *ᵥ x - b‖ ^ 2) ((fun x => Aᵀ *ᵥ (A *ᵥ x - b)) x₁) x₁

Tactic: exact (fun x => affine_sq_gradient x)

State after:

Relevant lemmas:
affine_sq_gradient : ∀ {n m : ℕ+} {b : Fin ↑m → ℝ} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} (x : EuclideanSpace ℝ (Fin ↑n)),
  HasGradientAt (fun x => 1 / 2 * ‖A *ᵥ x - b‖ ^ 2) (Aᵀ *ᵥ (A *ᵥ x - b)) x