theorem extracted_formal_statement_200 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} {Ane0 : A ≠ 0}
  (h_original_goal : 0 < ‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) (Aᵀ * A)‖₊) : ¬Aᵀ * A = 0 := sorry

State before:
case tpos
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
k : ℕ
⊢ 0 < ‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) (Aᵀ * A)‖₊

Tactic: simp

State after:
[case tpos
 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
 k : ℕ
 ⊢ ¬Aᵀ * A = 0]

Relevant lemmas: