theorem extracted_formal_statement_58 {n m : ℕ+} {b : Fin ↑m → ℝ} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ}
  (x : EuclideanSpace ℝ (Fin ↑n)) :
  let f := fun x => 1 / 2 * A *ᵥ x ⬝ᵥ A *ᵥ x;
  let f' := fun x => Aᵀ *ᵥ A *ᵥ x;
  HasGradientAt f (f' x) x →
    let h := fun x => b ⬝ᵥ A *ᵥ x;
    let h' := fun x => Aᵀ *ᵥ b;
    HasGradientAt h (h' x) x := sorry

State before:
n m : ℕ+
b : Fin ↑m → ℝ
A : Matrix (Fin ↑m) (Fin ↑n) ℝ
x : EuclideanSpace ℝ (Fin ↑n)
f : EuclideanSpace ℝ (Fin ↑n) → ℝ := fun x => 1 / 2 * A *ᵥ x ⬝ᵥ A *ᵥ x
f' : EuclideanSpace ℝ (Fin ↑n) → Fin ↑n → ℝ := fun x => Aᵀ *ᵥ A *ᵥ x
fgradient : HasGradientAt f (f' x) x
h : EuclideanSpace ℝ (Fin ↑n) → ℝ := fun x => b ⬝ᵥ A *ᵥ x
h' : EuclideanSpace ℝ (Fin ↑n) → Fin ↑n → ℝ := fun x => Aᵀ *ᵥ b
⊢ HasGradientAt h (h' x) x

Tactic: apply linear_gradient

State after:

Relevant lemmas: