theorem extracted_formal_statement_192 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} {Ane0 : A ≠ 0}
  (h_original_goal : ↑‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) (Aᵀ * A)‖₊ > 0) : ¬Aᵀ * A = 0 := 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
⊢ ↑‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) (Aᵀ * A)‖₊ > 0

Tactic: simp

State after:
[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
 ⊢ ¬Aᵀ * A = 0]

Relevant lemmas: