theorem extracted_formal_statement_9 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} (hA : A = 0)
  (x : EuclideanSpace ℝ (Fin ↑n)) (h_original_goal : HasGradientAt (fun x => A *ᵥ x ⬝ᵥ A *ᵥ x) (2 • Aᵀ *ᵥ A *ᵥ x) x) :
  HasGradientAt (fun x => 0 *ᵥ x ⬝ᵥ 0 *ᵥ x) (2 • 0ᵀ *ᵥ 0 *ᵥ x) x := sorry

State before:
case pos
n m : ℕ+
A : Matrix (Fin ↑m) (Fin ↑n) ℝ
hA : A = 0
x : EuclideanSpace ℝ (Fin ↑n)
⊢ HasGradientAt (fun x => A *ᵥ x ⬝ᵥ A *ᵥ x) (2 • Aᵀ *ᵥ A *ᵥ x) x

Tactic: rw [hA]

State after:
[case pos
 n m : ℕ+
 A : Matrix (Fin ↑m) (Fin ↑n) ℝ
 hA : A = 0
 x : EuclideanSpace ℝ (Fin ↑n)
 ⊢ HasGradientAt (fun x => 0 *ᵥ x ⬝ᵥ 0 *ᵥ x) (2 • 0ᵀ *ᵥ 0 *ᵥ x) x]

Relevant lemmas: